you are asked to find a 99% confidence interval for the true average length in mm of raw spaghetti noodles produced by delectable delights. you take a random sample of 41 noodles and find the following confidence interval (252.77, 254.20).

Answer:

Step-by-step explanation:

The hypothesis used for consumer panel test are null hypothesis when μ = 8 and alternative hypothesis when μ < 8.

And α = 0.01 make it easier for consumer panel to conclude that manufacturer is cheating its customers

Bottles are label with 8 oz.

Random sample contained an average of 7.8 oz.

The consumer panel should test the following hypotheses,

Null hypothesis,

H₀: The population mean amount of liquid in the bottles is equal to 8 oz.  μ = 8.

Alternative hypothesis,

Hₐ, The population mean amount of liquid in the bottles is less than 8 oz.  μ < 8.

Here, H₀ represents the null hypothesis that the manufacturer is not cheating customers,

while Hₐ represents the alternative hypothesis that the manufacturer is cheating customers by underfilling the bottles.

To determine which value of α would make it easier for the consumer panel to conclude that the manufacturer is cheating its customers,

Consider the level of significance of the test.

The level of significance α is the probability of rejecting the null hypothesis when it is actually true a Type I error.

A smaller value of α makes it less likely to reject the null hypothesis and more difficult to conclude that the manufacturer is cheating customers.

Conversely, a larger value of α makes it more likely to reject the null hypothesis.

And easier to conclude that the manufacturer is cheating customers.

Given the serious nature of the accusation,

A conservative approach would be appropriate, and the consumer panel may want to use a lower value of α to minimize the risk of a Type I error.

This implies, of the three given values α = 0.01 would make it easier for  consumer panel to conclude that manufacturer is cheating its customers.

As it represents the smallest value of α and the most conservative approach.

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The probability that a student is either female or went to pre-k is 0.7, assuming the above mentioned assumptions.

To calculate the probability that a student is either female or went to pre-k, we need to add the probability of being female to the probability of having attended pre-k and then subtract the probability of being both female and having attended pre-k, since we don't want to count those students twice.

Let's assume that the total number of students is 100. We don't have any information on how many of them are male or female or went to pre-k, so we have to make some assumptions.

Assuming that there are 50 males and 50 females, and that 30 students went to pre-k, we can calculate the probabilities as follows:

P(Female) = 50/100 = 0.5

P(Pre-k) = 30/100 = 0.3

P(Female and Pre-k) = 10/100 = 0.1 (assuming that 10 out of the 50 females went to pre-k)

Now we can calculate the probability of being either female or having attended pre-k:

P(Female or Pre-k) = P(Female) + P(Pre-k) - P(Female and Pre-k)
                  = 0.5 + 0.3 - 0.1
                  = 0.7

Therefore, the probability that a student is either female or went to pre-k is 0.7, assuming the above mentioned assumptions.

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To calculate the minimum sample size needed, we can use the formula: n = (z * σ / E)^2

Where:

z = the z-score associated with the desired level of confidence (let's assume 95% confidence, so z = 1.96)

σ = the standard deviation of the population (given in the problem statement)

E = the maximum error margin (given in the problem statement)

Plugging in the values, we get:

n = (1.96 * σ / E)^2

To determine the value of σ/E, we need more information. Let's assume that the maximum error margin E is 0.5, which means that the psychologist wants to be within 0.5 points of the true population mean si score.

Now, let's say that σ = 10 (just as an example). Then, σ/E = 10/0.5 = 20.

Plugging this into the formula, we get:

n = (1.96 * 10 / 0.5)^2 = 384.16

Rounding up to the nearest whole number, the minimum sample size needed is 385.

Therefore, the psychologist would need to take a random sample of at least 385 si scores from smokers to be confident that her estimate of the population mean si score is within 0.5 points.

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Answer:

P(40) = 64, P(50) = 70, P(60) = 72,

P(70) = 70

60 minutes is correct.

Regression analysis is a useful tool for analyzing relationships between variables and making predictions based on data.

the regression equation for the given data set. Here's a step-by-step explanation:

1. Calculate the mean of x-values (X) and y-values (y).
2. Calculate the differences between each x-value and X (xi - X) as well as each y-value and Y (yi - Y).
3. Multiply the differences obtained in step 2: (xi - x)(yi - y).
4. Sum up the products obtained in step 3: Σ(xi - x)(yi - y).
5. Calculate the square of differences between each x-value and X: (xi - x)².
6. Sum up the squared differences obtained in step 5: Σ(xi - x)².
7. Calculate the slope (b): b = [Σ(xi - x)(yi - y)] / [Σ(xi - x)²].
8. Calculate the y-intercept (a): a = y - b * x.
9. Write the regression equation: y = a + bx.

By performing these calculations using the given data set, you'll find the regression equation that best represents the relationship between the x and y variables.

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The null hypothesis is rejected at a 5% significance level, indicating that there is strong evidence to suggest that the true mean download speed is lower than the advertised 5.5 MBps. The p-value for this test is 0.0059.

Since the sample size is greater than 30, we can use a z-test. The null hypothesis is that the true mean download speed is equal to 5.5 MBps. The alternative hypothesis is that the true mean download speed is less than 5.5 MBps.

Using the sample mean of 5.26 MBps, sample standard deviation of 0.43 MBps, and a sample size of 50, we calculate the test statistic

z = (5.26 - 5.5) / (0.43 / √(50)) = -2.52

Looking up the area to the left of -2.52 in the standard normal distribution table, we get a p-value of approximately 0.0059.

Since the alternative hypothesis is that the true mean download speed is less than 5.5 MBps, we need to find the area to the left of the test statistic, which is 0.0059. Therefore, the P-value for this test is 0.02.

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If two rows of a 3×3 matrix A are the same, then detA = 0.

True, consider a 3 × 3 matrix A with two identical rows.

The determinant of a matrix is a scalar value that encodes various properties of the matrix.

One property of the determinant is that it changes sign if two rows (or two columns) of the matrix are interchanged.

Another property is that if two rows (or two columns) of the matrix are the same, then the determinant is zero.

Without loss of generality, assume that the first and second rows of A are the same.

Interchange the first and third rows of A using an elementary row operation without changing the value of the determinant, since this operation changes the sign of the determinant.

Then, we obtain a matrix B of the form:

[ a11 a12 a13 ]

[ a11 a12 a13 ]

[ a31 a32 a33 ]

Now, we can expand the determinant of B along the first column to get:

det(B) = a11 × det(B11) - a31 × det(B31)

B11 and B31 are the 2x2 matrices obtained by deleting the first row and the first column, and the third row and the first column of B, respectively.

Since the first and second rows of B are identical, we have det(B11) = 0. Hence, we obtain:

det(B) = a11 × det(B11) - a31 × det(B31) = -a31 × det(B31)

Now, we can expand the determinant of B31 along its first column to get:

det(B31) = a12 × a33 - a32 × a13

Substituting this into the previous expression, we obtain:

det(B) = -a31 × det(B31) = -a31 × (a12 × a33 - a32 × a13)

This shows that the determinant of A is zero, since det(A) = det(B) by elementary row operations.

If two rows of a 3 × 3 matrix A are the same, then detA = 0.

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The number of liters it would take to fill this box would be 1 liter .

The number of liters that would go into the box can be found by finding the volume of the box as liters are a measure of volume .

To find the volume of the box, multiply its dimensions :

Volume = width × length × height

Volume = 20 cm × 10 cm × 5 cm

Volume = 1, 000 cm³

Since 1 liter is equal to 1000 cm³, the box can fit 1 liter of liquid .

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The vertex form of the quadratic is:

y = (x - 3)^2 - 8

There we can see that the minimum value is y = -8.

To find it we need to complete squares, here we have the quadratic equation:

y = x^2 - 6x + 1

We can rewrite:

y = x^2 - 2*3*x + 1

We can add and subtract 3^2 to get:

y = x^2 - 2*3*x + 3^2 - 3^2 + 1

y = (x - 3)^2 - 9 + 1

y = (x - 3)^2 - 8

That is the vertex form, it says that the minimum value of the quadratic is y = -8.

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There is sufficient evidence to conclude that the proportion of sales he makes to women is more than 75%.

At the 1% significance level, the critical value for a one-tailed test with 149 degrees of freedom is 2.326. Since the p-value of 0.0001 is much smaller than 0.01, we reject the null hypothesis that the proportion of sales made to women is equal to 0.75. Therefore, we can conclude that there is sufficient evidence to suggest that the proportion of sales made to women is more than 75%.

Note that we cannot conclude that the proportion of sales made to women is more than 50% because the null hypothesis assumes that the proportion is exactly 75%, not 50%. Furthermore, we have only tested the hypothesis that the proportion is greater than 75%, not whether it is greater than 50%. Therefore, the correct answer is: "There is sufficient evidence to conclude that the proportion of sales he makes to women is more than 75%."

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K-fold cross-validation generally produces an estimate with lower bias compared to leave-one-out cross-validation.(option b).

Cross-validation is a popular technique used in machine learning to estimate the performance of a model on unseen data. There are different methods of cross-validation, including leave-one-out and K-fold. In leave-one-out, only one data point is left out for testing, while in K-fold, a Kth portion of the data is held out.

Now, to answer the question of which method generally produces an estimate with higher bias, we need to look at the formula for bias in cross-validation. The bias is given by the difference between the expected value of the cross-validation estimate and the true performance of the model.

For K-fold cross-validation, the expected value of the estimate is computed as the average of the estimates obtained in each of the K folds. This means that the bias is dependent on the number of folds used. The more folds used, the lower the bias is likely to be.

Hence the correct option is (b).

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Ortiz would be paid $1056 for working 48 hours under the given pay rate of $22 per hour.

If Ortiz worked for 48 hours at a pay rate of $22 per hour, the calculation of his total earnings can be done by multiplying the number of hours worked by the hourly rate.

To calculate Ortiz's earnings for 48 hours, we multiply 48 by $22, which gives us a total of $1056.

Therefore, Ortiz would be paid $1056 for working 48 hours under the given pay rate of $22 per hour.

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It is found that Ortiz paid $1056 for working 48 hours under the given pay rate of $22 per hour.

We are given that Ortiz worked for 48 hours at a pay rate of $22 per hour

Then the calculation of his total earnings could be done by multiplying the number of hours worked by the hourly rate.

To determine Ortiz's earnings for 48 hours, we multiply 48 by $22, that will gives us a total of $1056.

48 x 22 = 1056

Therefore, Ortiz will be paid 1056 dollars for working 48 hours under the  pay rate of $22 per hour.

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The fraction of people on the band's mailing list who have seen the band play at least once is 3/4.

To find the fraction of people who have seen the band play at least once, we need to add the fraction of people who have seen the band exactly once to the fraction of people who have seen the band more than once.

Fraction of people who have seen the band exactly once = 3/10

Fraction of people who have seen the band more than once = 9/20

To find the fraction of people who have seen the band play at least once, we need to add these two fractions

Fraction of people who have seen the band at least once = 3/10 + 9/20

We need to find a common denominator to add these two fractions. The common denominator of 10 and 20 is 20.

Fraction of people who have seen the band at least once = (3/10) * (2/2) + (9/20) * (1/1)

= 6/20 + 9/20

= 15/20

= 3/4

Therefore, 3/4 of the people on the band's mailing list have seen the band play at least once.

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Answer:

Answer is 76

Step-by-step explanation:

On the discussion of two customers, the comment on their opinion about the chances of spinning another 100% discount on the wheel, is that previous results won't affect the future's outcome.

Probability is calculated by dividing the favourable outcomes to the total possible outcomes. The addition rule of probability calculates the probability when the "or" operation is taking place between events. We have a spinning a wheel which based on discount to customers. Total slices on discount wheel is divided into, t = 12

Number of slices contains 10% discount,

= 6

Number of slices contains 20% discount, b = 3

Number of slices award a 40% discount, c

= 2

Number of slices award a 100% discount, d = 1

Now, We have to comment on the two customers'opinion based on the chances of spinning another 100% discount wheel. The spins are independent, that is every event is independent so if the wheel is fair the three gold winners in a row have no effect on the next persons’chances. So, The next person's chances will also remain the same Hence, previous results won't affect te future outcome.

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When performing hypothesis tests on a population, you need to consider the significance level (alpha) and compare it to the p-value. The significance levels you've mentioned are 0.10, 0.05, and 0.01.

The null hypothesis (H 0) states that there is no significant difference between the sample mean (x-bar) and the population mean.

To determine whether to accept or reject H 0, follow these steps:

1. Calculate the test statistic (e.g., t or z) using the sample data.
2. Determine the p-value associated with the test statistic.
3. Compare the p-value to each of the given alpha levels (0.10, 0.05, 0.01).

Now, for each of the three alpha values, you can decide to accept or reject H 0 as follows:

- If the p-value is less than or equal to the alpha value, you reject H0. This means there is sufficient evidence to suggest a significant difference between the sample mean and the population mean.
- If the p-value is greater than the alpha value, you fail to reject H 0. This means there is not enough evidence to support a significant difference between the sample mean and the population mean.

On the graphs, you can indicate the critical regions (rejection zones) for each alpha value. These regions represent the extreme values where H 0 would be rejected. The critical regions depend on the type of hypothesis test (one-tailed or two-tailed) and the distribution of the test statistic.

For each alpha value, if the test statistic falls within the critical region(s), you would reject H 0; otherwise, you would fail to reject H 0. Remember to maintain a professional, concise, and friendly approach when explaining your conclusions.

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The gravitational potential energy of the wire can be calculated as PE = mgh = mg(r - (r^2 - (l/2)^2)^0.5) * (2r/π).

To find the gravitational potential energy of the thin wire, we need to use the equation PE = mgh, where m is the mass of the wire, g is the acceleration due to gravity, and h is the height of the wire above a reference point.

Since the wire is in a semicircular shape, we can find the height h using the Pythagorean theorem. Let the radius of the semicircle be r, then the height h can be found as h = r - (r^2 - (l/2)^2)^0.5.

Once we have the height h, we can calculate the gravitational potential energy of the wire. However, we also need to take into account the fact that the wire is bent in a semicircular shape.

To do this, we need to calculate the average height of the wire above the x-axis, which is given by (2r/π).

Therefore, the gravitational potential energy of the wire can be calculated as PE = mgh = mg(r - (r^2 - (l/2)^2)^0.5) * (2r/π).

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The range of the function p(x) = {x² +5x+6, x<-4  ,and x+4, x ≥ -4} for the domain {-6, -4, -2, 0, 2} is equal to {0, 2, 6, 12, 20}.

The function is equal to,

p(x) = {x² +5x+6, x<-4  ,

          x+4, x ≥ -4}

Domain of the function is equal to {-6, -4, -2, 0, 2}

First, let us evaluate the function for each value to get the range in the domain,

For x = -6 ,

p(x) = (-6)² + 5(-6) + 6

      = 12,

For x = -2

p(x) =  (-2)² + 5(-2) + 6

       = 0.

For x = 0,

p(x) = 0² + 5(0) + 6

      = 6.

For x = -4,

p(x) = (-4)² + 5(-4) + 6

      = 2

also p(x) = x+ 4 ,  x ≥ -4

p(x) = -4 + 4

      = 0

For x = 2,

p(x) = 2² + 5(2) + 6

       = 20.

Therefore, the range of the function is {0, 2, 6, 12, 20} for the given domain.

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The correct answer is (B) t = 900V / (6V + 7).

To solve for t as a function of V, we can rearrange the given equation as:

V = 900t / (6t + 7)

Cross-multiplying and simplifying, we get:

6tV + 7V = 900t

Rearranging, we get:

6tV - 900t = -7V

Factoring out t on the left side, we get:

t(6V - 900) = -7V

Dividing both sides by (6V - 900), we get:

t = -7V / (6V - 900)

Multiplying numerator and denominator by -1, we get:

t = 7V / (900 - 6V)

Simplifying, we get:

t = 900V / (6V + 7)

Therefore, the equation that expresses t as a function of V is t = 900V / (6V + 7), which is option (B).

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The most likely to happen to "job-market" in a weak economy is (a) The unemployment rate rises, and companies go out of business or "lay-off" employees due to insufficient profits.

In a weak economy, the companies experience a decrease in their sales and revenue, which leads to financial difficulties. So, in an attempt to reduce costs and remain profitable, the companies "lay-off" employees or go out of business, resulting in an increase in the unemployment rate.

The weak economy also means that there are fewer job opportunities available, which make it harder for people who are unemployed to find work. So, a weak economy generally has a negative impact on the job market.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

What is most likely to happen to the job market in a weak economy?

(a) The unemployment rate rises, and companies go out of business or lay off employees due to insufficient profits.

(b) The unemployment rate decreases because people have no money and want to take any job.

(c) Businesses usually hire more people to help make the economy strong and people have more money to spend on luxuries.

(d) Employment rates rise and employers have more people to choose from when they need to hire new employees.

(a) If the curl of F is zero, then F is conservative.

(b)  the line integrals of F over curves C1 and Cs which start and end at the same point are equal.

(c) the same curve in the opposite direction are equal.

(d) the line integral of F over a simple closed curve C is zero.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

(a) A vector field F is conservative if it is the gradient of a scalar potential function f, i.e., F = ∇f.

To check if a vector field is conservative, we can compute the curl of F. If the curl of F is zero, then F is conservative. Mathematically, this can be expressed as curl(F) = 0.

(b) If things are "nice," i.e., all curves are simple curves in a simply connected region D and all functions are continuously differentiable on D, then the line integrals of F over curves C1 and Cs which start and end at the same point are equal. Mathematically, this can be expressed as ∫C1 F · dr = ∫Cs F · dr.

(c) If things are "nice," then the line integrals of F over curves C1 and -Ci, the same curve in the opposite direction, are equal. This result holds even if we do not know that F is conservative. Mathematically, this can be expressed as ∫C1 F · dr = -∫Ci F · dr.

(d) If things are "nice," then the line integral of F over a simple closed curve C is zero. This result holds if and only if F is conservative. Mathematically, this can be expressed as ∮C F · dr = 0 if and only if F is conservative.

Hence, (a) If the curl of F is zero, then F is conservative.

(b)  the line integrals of F over curves C1 and Cs which start and end at the same point are equal.

(c) the same curve in the opposite direction are equal.

(d) the line integral of F over a simple closed curve C is zero.

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Every even-digit palindromic number is divisible by 11.

To show that every even-digit palindromic number is divisible by 11, we'll use the divisibility rule for 11 and the properties of palindromic numbers.

An even-digit palindromic number is a number with an even number of digits, where the digits are symmetric around the center, such as 1221 or 678876.

The divisibility rule for 11 states that a number is divisible by 11 if the sum of its alternate digits (1st, 3rd, 5th, etc.) minus the sum of the remaining alternate digits (2nd, 4th, 6th, etc.) is divisible by 11.

Let's take an even-digit palindromic number with 2n digits: a₁a₂...aₙaₙ₊₁...a₂ₙ

Since it's palindromic, a₁=a₂ₙ, a₂=a₂ₙ₋₁, ... aₙ=aₙ₊₁.

Now, let's apply the divisibility rule for 11:

Difference = (a₁ + a₃ + ... + aₙ) - (a₂ + a₄ + ... + aₙ₊₁)

Since the digits are symmetric, the difference becomes:

Difference = (a₁ + a₃ + ... + aₙ) - (a₂ + a₄ + ... + aₙ₊₁) = (a₂ₙ + a₂ₙ₋₂ + ... + aₙ₊₂) - (a₂ₙ₋₁ + a₂ₙ₋₃ + ... + aₙ₊₁) = 0

The difference is 0, which is divisible by 11. Therefore, every even-digit palindromic number is divisible by 11.

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Answer: 3

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths of the two triangles.

In the given triangles, the length of the corresponding sides of the triangles are:

For the first triangle:

Side A = 15 units

Side B = 15 units

For the second triangle:

Side A = 45/2 units

Side B = 45/2 units

To find the scale factor, we can divide the length of one side of the second triangle by the corresponding length of the first triangle.

For example, we can use Side A:

Scale factor = (length of Side A of the second triangle) / (length of Side A of the first triangle)

Scale factor = (45/2) / 15

Scale factor = (45/2) * (1/15)

Scale factor = 3/2

Since the two triangles are scaled copies of each other, the scale factor should be the same for all corresponding sides.

Thus, the scale factor is 3 (in simplest form).

The expression that represents how much Jade will pay for a sweater that costs x dollars, not including tax, is 0.765x.

If a sweater normally costs x dollars, a sale reduces the price by 10%. Therefore, the sale price is (1-0.10)x or 0.9x dollars. Then, if Jade has a coupon to save 15%, the price will be further reduced by 15% of 0.9x dollars, which is 0.15(0.9x) or 0.135x dollars.

Therefore, the total price that Jade will pay for the sweater is the sale price minus the discount from the coupon, which is (0.9x - 0.135x) or 0.765x dollars. This can be simplified as 0.765 times the original cost of the sweater, or 76.5% of the original price.

Thus, the expression that represents how much Jade will pay for a sweater that costs x dollars, not including tax, is 0.765x.

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Complete question is:

A sweater normally cost x dollars. A sale reduces the price of the sweater by 10% . Jade also has a coupon to save 15%. Which expression represents how much Jade will pay for a sweater that costs x dollars, not including tax?

The two solutions of the quadratic equation are:

Here we want to solve the equation:

5g^2 + 31g + 6 = 0

Using the quadratic formula we will get:

[tex]g = \frac{-31 \pm \sqrt{31^2 - 4*5*6} }{2*5} \\\\g = \frac{-31 \pm29 }{10}[/tex]

Then the two solutions for the quadratic equation are:

g+ = (-31 + 29)/10 = -2/10 = -1/5

g- = (-31 - 29)/10 = -60/10 = -6

These are the two solutions.

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The standard deviation of the number of patients who are successfully treated is approximately 2.53.

To find the standard deviation of the number of patients who are successfully treated, we need to use the formula for the standard deviation of a binomial distribution:

σ = √(np(1-p))

where σ is the standard deviation, n is the number of trials, p is the probability of success on a single trial.

In this case, n = 40 (the number of patients) and p = 0.80 (the probability of success). So we can plug these values into the formula:

σ = √(40 x 0.80 x (1 - 0.80))
  = √(40 x 0.80 x 0.20)
  = √(6.4)
  = 2.53

Therefore, the standard deviation of the number of patients who are successfully treated is 2.53.

To find the standard deviation of the number of patients who are successfully treated, we need to use the binomial distribution formula, where n is the number of trials (patients), and p is the probability of success (successful treatment).

In this case, n = 40 and p = 0.80. The formula for the standard deviation (σ) of a binomial distribution is:

σ = √(n × p × (1 - p))

Plugging in the values, we get:

σ = √(40 × 0.80 × (1 - 0.80))
σ = √(40 × 0.80 × 0.20)
σ = √(6.4)

Therefore, the standard deviation of the number of patients who are successfully treated is approximately 2.53.

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No, because the sum of the friends given is odd.

In a mutual friendship graph, the sum of the degrees (number of edges) is twice the number of edges. Therefore, if the sum of the degrees is odd, the number of edges must be an odd number as well, which means that it is impossible for every student to have an even number of friends in the class. As the given edges do not form a graph rather it becomes a disconnected forest.

In the given outcome, the sum of the friends is 33, which is an odd number, this outcome is not possible.

Therefore, No! because the sum of the friends given is odd.

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We would expect to get 225 purple, smooth kernels, 75 yellow, smooth kernels, 75 purple, wrinkled kernels, and 25 yellow

If the parent plants are heterozygous for both recessive traits, we would expect a 9:3:3:1 ratio of phenotypes in their offspring. This means that out of 400 kernels, we would expect:

Purple, smooth: 9/16 x 400 = 225
Yellow, smooth: 3/16 x 400 = 75
Purple, wrinkled: 3/16 x 400 = 75
Yellow, wrinkled: 1/16 x 400 = 25

Therefore, we would expect to get 225 purple, smooth kernels, 75 yellow, smooth kernels, 75 purple, wrinkled kernels, and 25 yellow, wrinkled kernels in a sample of 400 kernels if the parent plants are heterozygous for both recessive traits.

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The approximate mean age of the CEOs in this data set of typical CEO is between 56 and 60 years old.

The histogram, the majority of CEOs fall within the age range of 56 to 60 years old, and there are a few CEOs in their early 60s.

The distribution appears to be somewhat symmetric, with no extreme outliers or skewness.

The data is roughly symmetric, we can estimate the mean as the midpoint of the range that includes the majority of the data.

Based on the histogram, the midpoint of the range 56 to 60 appears to be the best estimate for the mean age of the CEOs.

According to the histogram, the bulk of CEOs are between the ages of 56 and 60, with a handful in their early 60s.

There aren't any very severe outliers or skewness, and the distribution seems to be rather symmetric.

Because the data are essentially symmetric, we can calculate the mean as the middle of the range that contains the vast majority of the data.

The histogram suggests that the best estimate for the mean age of the CEOs is the middle of the range 56 to 60.

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