a research methods student wants to test for differences between the mean social skills scores of psychology, chemistry, and philosophy majors. which of the following is the appropriate null hypothesis test?a. one-way ANOVAb. test of Pearson'sc. paired samples t testd. independent-samples t test

Therefore, the required probabilities are:

a) P(red car) = 0.537

b) P(speeding ticket) = 0.546

c) P(speeding ticket | red car) = 0.421

d) P(red car | speeding ticket) = 0.413

e) P(red car and speeding ticket) = 0.226

f) P(red car or speeding ticket) = 0.857

a) The probability that a randomly chosen person has a red car is the number of people with red cars divided by the total number of people, which is:

P(red car) = 335/624

= 0.537 (rounded to the nearest thousandth).

b) The probability that a randomly chosen person has a speeding ticket is the number of people with speeding tickets divided by the total number of people, which is:

P(speeding ticket) = 341/624

= 0.546 (rounded to the nearest thousandth).

c) The probability that a randomly chosen person has a speeding ticket given they have a red car is the number of people with red cars and speeding tickets divided by the number of people with red cars, which is:

P(speeding ticket | red car) = 141/335

= 0.421 (rounded to the nearest thousandth).

d) The probability that a randomly chosen person has a red car given they have a speeding ticket is the number of people with red cars and speeding tickets divided by the number of people with speeding tickets, which is:

P(red car | speeding ticket) = 141/341

= 0.413 (rounded to the nearest thousandth).

e) The probability that a randomly chosen person has a red car and got a speeding ticket is the number of people with red cars and speeding tickets divided by the total number of people, which is:

P(red car and speeding ticket) = 141/624

= 0.226 (rounded to the nearest thousandth).

f) The probability that a randomly chosen person has a red car or got a speeding ticket is the sum of the probabilities of having a red car and having a speeding ticket minus the probability of having both, which is:

P(red car or speeding ticket) = P(red car) + P(speeding ticket) - P(red car and speeding ticket)

= 0.537 + 0.546 - 0.226

= 0.857 (rounded to the nearest thousandth).

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The standard deviation for the random variable X, the number of wins, is approximately 0.10341.

Probability of winning a certain lottery [tex]= 1/51,949[/tex]

560 times were played overall.

Let X represent the random variable that represents the number of victories out of 560 plays.

The probability of winning in one play is [tex]p = 1/51,949[/tex]. The probability of not winning in one play is [tex]q = 1 - p[/tex]

[tex]q = (51,949 - 1) / 51,949[/tex]

[tex]q = 51,948 / 51,949.[/tex]

What X should actually be is:

[tex]E(X) = np[/tex]

[tex]E(X) = 560 * (1/51,949)[/tex]

[tex]E(X) = 0.010793[/tex]

The variance of X is:

[tex]Var(X) = npq[/tex]

[tex]Var(X) = 560 * (1/51,949) * (51,948/51,949)[/tex]

[tex]Var(X) = 0.010699[/tex]

The value of X's standard deviation is

[tex]SD(X) = \sqrt{Var(X)}[/tex]

[tex]SD(X) = \sqrt{0.010699}[/tex]

[tex]SD(X) = 0.10341[/tex](approx)

Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.

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The possible values of the sum of a, b and c is (c) - 14

From the question, we have the following parameters that can be used in our computation:

Vertex = (9, -14)

It intersects the x-axis at two points.

So, we have (x₁, 0) and (x₂, 0)

The equation of a parabola in vertex form is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

So, we have

y = a(x - 9)² - 14

Expanding the equation, we have

y = a(x² - 18x + 81) - 14

Open the brackets

This gives

y = ax² - 18ax + 81a - 14

Set a = 0

So, we have

y = (0)x² - 18(0)x + 81(0) - 14

Evaluate

y = 0x² - 0x - 14

This means that

a = 0

b = 0

c = -14

Add the constants a, b and c

So, we have

Sum of constant = 0 + 0 - 14

Evaluate the sum

Sum of constant = - 14

Hence, the possible value of a + b + c is -14

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The volume of solid generated by rotating the region bounded by curves y = ln( 3x), y = 2, y = 3, x= 0; about the y-axis is equals to the [tex] \frac{π}{18}({e^6}- e^4)[/tex]. The volume of solid generated by rotating the region bounded by curves = 9x⁶, y = 9x, x ≥0; about x-axis is equals to the [tex]\frac{81π}{13} \\ [/tex].

We have a solid obtained by rotating the region bounded by the curves with equations, y = ln 3x, y = 2, y = 3, x= 0; about the specified line, y-axis. We have to determine the volume, V of that solid. First, see the above diagram where red line, green line, blue line and purple lines represent y = ln 3x, y = 3, y = 2, x= 0 respectively. The volume of shaded region will be determine. Using formula, [tex]V = \int_{y = 2}^{y = 3} πx² dy \\ [/tex]

Now, y = ln( 3x)

taking exponential both sides,

[tex]e^ y = 3x [/tex]

[tex]x = \frac{ e^y}{3}[/tex]

so, [tex]V = \int_{y = 2}^{y = 3} π ( \frac{e^y}{3})² dy \\ [/tex]

[tex]= \int_{y = 2}^{y = 3} π ( \frac{e^{2y}}{9})dy \\ [/tex]

[tex]=[π(\frac{e^{2y}}{9 \times 2})]_{2}^{3} [/tex]

[tex]= π ( \frac{e^6}{18} -\frac{ e^4}{18})[/tex]

[tex]= \frac{π}{18}({e^6}- e^4)[/tex]

Hence, required value is [tex]= \frac{π}{18}({e^6}- e^4)[/tex].

Solid obtained by rotating the region bounded by the curves with equations, y = 9x⁶, y = 9x, x ≥0; about the specified line, x-axis. We have to determine the volume, V of that solid. First we determine the intersection points of y = 9x² and y = 9x

=> 9x = 9x²

=> x = 1

Using the formula, [tex]V = \int_{x= 0}^{x = 1} πy² dx \\ [/tex]

[tex] = \int_{x= 0}^{x = 1} π(9x⁶)² dx \\ [/tex]

[tex] = \int_{x= 0}^{x = 1} 81πx¹² dx \\ [/tex]

[tex] = 81π [ \frac{x¹³}{13}]_{x= 0}^{x = 1} \\ [/tex]

[tex] = 81π [ \frac{1¹³}{13} - 0] \\ [/tex]

[tex] = \frac{81π}{13} \\ [/tex]. Hence, required value is [tex]\frac{81π}{13} \\ [/tex].

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To subtract 1/2h-1 from 3/4h+4, we can distribute the negative sign to the expression 1/2h-1 and then combine like terms. This gives:

(3/4h + 4) - (1/2h - 1)

= 3/4h + 4 - 1/2h + 1 (distributing the negative sign)

= (3/4h - 1/2h) + (4 + 1) (combining like terms)

= 1/4h + 5

Therefore, the result of subtracting 1/2h-1 from 3/4h+4 is 1/4h+5.

Slope of the normal L is 21/8.

Hence the correct option is (A).

Slope of normal to a function f(x) = y is given by = -dx/dy

Given the equation of the curve is,

2xy² - 3y = 18

Differentiating the function with respect to 'x' we get,

2x*2y*dy/dx + 2y²*1 - 3 dy/dx = 0

4xy*dy/dx + 2y² - 3dy/dx = 0

(3 - 4xy)dy/dx = 2y²

dy/dx = 2y²/(3 - 4xy)

-dx/dy = (4xy - 3)/2y²

Slope of the normal L at the point (3, 2) = (4*3*2 - 3)/(2*2²) = (24 - 3)/8 = 21/8

Hence the correct option is (A).

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The cost of walking this guest is $190.

The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.

The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.

In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.

Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.

Therefore, the total cost incurred by the hotel for walking the guest is:

$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190

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Answer:

2, 3, 1, 3, 5, 4---->1, 2, 3, 3, 4, 5

The median is 3.

The distinction between real variables and nominal variables is based on the type of measurement used to represent the variable.

A variable is a characteristic that can take different values or levels. Real variables are measured on a numerical scale and can take any value within a certain range.

On the other hand, nominal variables are categorical variables that represent non-numerical attributes. They are used to classify data into different groups or categories based on their characteristics. Examples of nominal variables include gender, race, nationality, and occupation. These variables cannot be measured using a numerical scale, but they can be represented using labels or codes.

The distinction between real variables and nominal variables is important because they require different methods of analysis. Real variables can be analyzed using statistical methods such as mean, standard deviation, and correlation, while nominal variables require different methods such as frequency tables and chi-square tests.

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Answer:

B No solution

Step-by-step explanation:

The probability of P(3 < X ≤ 6) is approximately 0.6575.

The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

To find P(3 < X ≤ 6), where X represents the number of times heads is tossed when a fair coin is tossed 10 times, we need to calculate the probability of obtaining more than 3 but less than or equal to 6 heads.

Since the coin is fair, the probability of getting heads on any single toss is 0.5, and the probability of getting tails is also 0.5.

We can use the binomial probability formula to calculate the probability for a specific number of heads in a given number of coin tosses:

P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^{(n-k)[/tex],

where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.

In this case, n = 10 (10 coin tosses), p = 0.5 (probability of heads), and we want to calculate the probability for 4, 5, and 6 heads.

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6)

Using the binomial probability formula, we can calculate these probabilities:

P(X = 4) = (10 choose 4) * [tex](0.5^4) * (0.5^6)[/tex] = 210 * 0.0625 * 0.015625 = 0.2063

P(X = 5) = (10 choose 5) * [tex](0.5^5) * (0.5^5)[/tex] = 252 * 0.03125 * 0.03125 = 0.2461

P(X = 6) = (10 choose 6) * [tex](0.5^6) * (0.5^4)[/tex] = 210 * 0.015625 * 0.0625 = 0.2051

Finally, we can calculate the desired probability:

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2063 + 0.2461 + 0.2051 = 0.6575

Therefore, P(3 < X ≤ 6) is approximately 0.6575.

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An image that has reflectional, rotational, and point symmetry is a regular polygon. I can explain the terms and help you identify the symmetries in the images.

1. Reflectional symmetry: An image has reflectional symmetry if it can be reflected over a line (called the "line of symmetry") and still look the same as the original image.

2. Rotational symmetry: An image has rotational symmetry if it can be rotated around a point (called the "center of rotation") by a certain angle (less than 360°) and still look the same as the original image.

3. Point symmetry: An image has point symmetry if it looks the same when rotated by 180° around a central point (also called the "point of symmetry").

To determine which image has all three types of symmetry, examine each image and check if it meets the criteria for reflectional, rotational, and point symmetry. Once you identify an image that satisfies all three criteria, you have found the correct image.

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Answer:

Yes, the function is exponential.

Step-by-step explanation:

The "^" represents an exponet. If you want to know, the exponent is 3.

The axis of symmetry of a parabola with vertex (5, -10) is x = 5, which is a vertical line passing through the vertex.

The axis of symmetry of a parabola is a vertical line that passes through its vertex and divides the parabola into two mirror-image halves. In this case, the vertex of the parabola is given as (5, -10), which means the vertex lies on a horizontal line passing through the axis of symmetry.

The equation of the axis of symmetry can be written as x = h, where (h, k) is the vertex of the parabola.

As from the given points h corresponds to value '5'. Therefore, the axis of symmetry for this parabola is x = 5, which is a vertical line passing through the point (5, -10).

To visualize this, you can imagine folding the parabola along its axis of symmetry. The left and right halves of the parabola will overlap perfectly, creating a symmetrical shape.

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Answer:480cm^3

Step-by-step explanation:

The arithmetic sequence is given by the expression A = 5 + 4n

Given data ,

Let the number sequence be represented as A

Now , the value of A is

A = 5 + 9 + 13 + 17 + 21 ...

On simplifying , we get

The first term of the series is a₁ = 5

Let the second term be a₂ = 9

So , the common difference d = a₂ - a₁

d = 9 - 5 = 4

And , let the number of terms be n

So , the expression is

A = 5 + 4n

when n = 4

A = 5 + 4 ( 4 ) = 25

Hence , the arithmetic sequence is A = 5 + 4n

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The simplified form of expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex] is  [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex]

The correct answer is an option (B)

Consider an expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex]

Multiply the fraction by an expression to form a perfect square in the denominator.

[tex]\sqrt[4]{\frac{3}{2x} }[/tex]

[tex]=\sqrt[4]{\frac{3\times 2^3\times x^3}{2x\times 2^3\times x^3} }[/tex]

We know that the cube of 2 is 8. So, substitute 2³ = 8

[tex]=\sqrt[4]{\frac{3\times 8\times x^3}{2x\times 8\times x^3} }[/tex]

Now, we multiply the monomials.

[tex]=\sqrt[4]{\frac{24\times x^3}{16\times x^4} }[/tex]

We know that the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex]

[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{16\times x^4} }[/tex]

We know that 2⁴ = 16

[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4\times x^4} }\\\\=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4}\times \sqrt[4]{x^4} }[/tex]        ............(using the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex])

[tex]=\frac{\sqrt[4]{24\times x^3}}{2x }[/tex]           .......(Simplify the radical expressions)

Here, [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex] is the simplified form of expression.

Therefore, the correct answer is an option (B)

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Find the complete question below.

Yes.

The data are from a random sample, meeting the Randomization Condition.

The data have at least 10 successes and 10 failures, meeting the Success/Failure Condition.

The population is much larger than the sample, meeting the 10% Condition. A

It is reasonable for the research team to use a Normal model for the sampling distribution of the sample proportion.

A Normal model for the sampling distribution of a sample proportion, three conditions must be met:

The Randomization Condition, the Success/Failure Condition, and the 10% Condition.

The Randomization Condition is met as the sample is selected randomly from a much larger population of adults.

The Success/Failure Condition is also met because the sample size is large enough (n = 1900) for us to expect at least 10 successes (those who are pessimistic about the future of marriage and family) and 10 failures (those who are optimistic about the future of marriage and family).

The sample proportion of pessimistic adults is 34%, which corresponds to 646 successes in the sample.

The 10% Condition is also met as the sample size (n = 1900) is less than 10% of the total population of adults.

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We have the height of the rectangle equal to h = 37.5 inches.

A rectangle is actually about a right triangle. We can use the Pythagorean theorem to generate an expression to find the height of the rectangle.

We know that:

[tex]c^2=a^2+b^2[/tex] so replacing it with the width and length of the rectangle, we get :

[tex]c^2=h^2+w^2[/tex]

We were not given values for the width and length, just their relationship to each other, and we can use that to find an equation in the variable h:

So, [tex]c^2=h^2+w^2[/tex]

[tex](56)^2=h^2+(h+4)^2[/tex]

[tex]3136=h^2+h^2+8h+16[/tex]

[tex]0=2h^2+8h+16-3136[/tex]

[tex]0=2h^2+8h-3,120[/tex]

Since we cannot factor this, we can use the quadratic formula to solve for the height h, where, a = 2 , b = 8, c = -3,120

h = (-b ±[tex]\sqrt{b^2-4ac}[/tex]) /2a

Now, Plug all the values:

h = (-8 ± [tex]\sqrt{8^2-4(2)(-3120)})/4[/tex])

h = -8 ± [tex]\sqrt{64+24,960}/4[/tex]

h =( -8 ± [tex]\sqrt{25,024})/4[/tex]

h = (-8 ± 158.180)/4

There are two possible solutions, so we have:

[tex]h_1=\frac{-8+158.180}{4}[/tex]                      [tex]h_2=\frac{-8-158.180}{4}[/tex]

[tex]h_1 = 37.545[/tex]                           [tex]h_2=-41.545[/tex]  

[tex]h_1[/tex] ≈ 37.5 in.                          [tex]h_2[/tex] ≈ -41.5 in.

We cannot use [tex]h_2[/tex] because a negative height is absurd and undefined. Thus, we have the height of the rectangle equal to h = 37.5 inches.

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In a case whereby there is a spinner with three equal sections colored red, white, and blue the  P(yellow) is 33%

Probability can be described as trhe act of showing how likely something is to happen it should be noted that this usually comes into play when we were not sure about the outcome of an event,  and the analysis of events governed by probability can be regarded as statistics.

P(yellow) =  1/3

= 0.33

0.33 * 100

= 33 percent

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The independent variable in this scenario is the number of guests that will be attending the cookout. The number of hot dogs needed is dependent on the number of guests, as the coach plans to provide two hot dogs for each guest and an additional 8 hot dogs for potential extra guests.

. In this situation, the coach needs to determine the number of hot dogs required for the cookout based on the number of guests. Let's represent the number of guests as "g" (independent variable) and the total number of hot dogs needed as "h" (dependent variable).

The coach wants 2 hot dogs for each guest and 8 extra hot dogs. So, the equation would be:

h = 2g + 8

In this equation, the independent variable is "g" (number of guests) because the total number of hot dogs needed (dependent variable "h") depends on how many guests are attending the cookout.

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The given series 2/8 + 4/9 + 6/10 + 8/11 + 10/12 + ..... is a divergent series.

The given series is:

2/8 + 4/9 + 6/10 + 8/11 + 10/12 + .....

Here,

t₁ = 2/8 = (2*1/(1 + 7))

t₂ = 4/9 = (2*2/(2 + 7))

Proceeding in this manner we get the n th term of the given series,

tₙ = (2*n)/(n + 7)

So, now the limit of n th term of the series is given by,

[tex]\lim_{n \to \infty}[/tex] tₙ = [tex]\lim_{n \to \infty}[/tex] (2*n)/(n + 7)) = [tex]\lim_{n \to \infty}[/tex] 2/(1 + 7/n)

Since n tends to infinity

So, 1/n tends  to 0. Let 1/n = y

So, 'y' tends to 0.

= [tex]\lim_{y \to 0}[/tex] 2/(1 + 7y) = 2 ≠ 0

Now, difference between (n+1)th and n th term is

= [tex]b_{n+1} - b_n[/tex]

= 2(n+1)/(n +1 +7) - 2n/(n + 7)

= (2(n + 1 + 7) - 14)/(n +1 +7) - (2(n + 7) - 14)/(n + 7)

= 2 - 14/(n + 8) - 2 + 14/(n +7)

= 14/(n +7) - 14/(n +8)

= 14(n + 8 - n - 7)/(n +7)(n +8)  

= 14/(n + 7)(n+8) > 0

So, [tex]b_{n+1}\geq b_n[/tex]

Hence the given series diverges.

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To determine if the criteria for approximate normality is met, we need to check if both the sample size and sample proportion are large enough. The sample size is n = 11,954 which is greater than 10.

Additionally, the sample proportion of landing on its right side is p = 0.571 which is also greater than 10. Therefore, the criteria for approximate normality is met.

A 99% confidence interval would be wider than the 90% confidence interval. This is because a higher confidence level requires a larger range to ensure the true population proportion is captured within the interval with a higher degree of certainty.

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The amount in the savings account after each number of years are as follows

2 years = $3413.6

5 years = $3434

8 years = $3454.4

In Mathematics, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

By substituting the given parameters into the simple interest formula, we have;

SI = 3400 × 0.2/100 × 2

SI = $13.6

A = SI + P = 13.6 + 3400 = $3413.6

After 5 years, we have:

SI = 3400 × 0.2/100 × 5

SI = $34

A = SI + P = 34 + 3400 = $3434

After 8 years, we have:

SI = 3400 × 0.2/100 × 8

SI = $54.4

A = SI + P = 54.4 + 3400 = $3454.4

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Complete Question:

Charlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.

2 years $

5 years $

8 years $

From the given decimals which are 0.2, 0.019, 0.12, 0.02, the smallest number is 0.019.

To compare the given decimals, we need to look at the digits to the right of the decimal point. Starting from the left, the first decimal is 0.2, which has one decimal place. The second decimal is 0.019, which has three decimal places. The third decimal is 0.12, which has two decimal places. Finally, the fourth decimal is 0.02, which has two decimal places.

To compare them, we can line them up vertically by decimal place and see which one has the smallest value in the first decimal place. In this case, the smallest value in the first decimal place is 0.019. Therefore, 0.019 is the smallest decimal among the given options.

In summary, the decimals listed from smallest to largest are: 0.019, 0.02, 0.12, 0.2.

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The expressions are equivalent to the given expression are x + x + 6 – 7 + x and 3 – x + 2x – 4 + 2x. Therefore, the options A and C are correct answer.

The given expression is 6+(-x)+2x+(-7)+2x.

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Here, group the like terms, we get

(-x+2x+2x)+(6-7)

= 3x-1

Therefore, the options A and C are correct answer.

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Answer:

yo

Step-by-step explanation:

the answers are A and C

x + x + 6 – 7 + x and  3 – x + 2x – 4 + 2x

Edge 2023

Answer:

5

Step-by-step explanation:

Given a=12 and c=13,

b = 5

∠α = 67.38° = 67°22'48" = 1.17601 rad

∠β = 22.62° = 22°37'12" = 0.39479 rad

h = 4.61538

area = 30

perimeter = 30

inradius = 2

circumradius = 6.5

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

To find the probability that less than 3 households have board games, we can use the binomial probability formula. The terms involved in this problem are:

1. n: number of trials (households)
2. k: number of successful outcomes (households with board games)
3. p: probability of success (having board games)
4. q: probability of failure (not having board games)

Given that 75% of households have board games, p = 0.75, and q = 1 - p = 0.25. In this case, n = 10 households. We need to find the probability of k = 0, 1, or 2 households having board games.

The binomial probability formula is:
P(X = k) = C(n, k) * p^k * q^(n-k)

Step 1: Calculate the probability for k = 0, 1, and 2 separately:
P(X = 0) = C(10, 0) * 0.75^0 * 0.25^10
P(X = 1) = C(10, 1) * 0.75^1 * 0.25^9
P(X = 2) = C(10, 2) * 0.75^2 * 0.25^8

Step 2: Add the probabilities for k = 0, 1, and 2 to get the total probability:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

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The polynomial is P(x)= 2/5x(x-4)²(x+4)

What in mathematics is a polynomial?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.

If the polynomial has a root of multiplicity 2 at  x=4, the (x−4)² is a factor.

Multiplicity 1 at x=0, then x is a factor.

Multiplicity 1 at x= -4 then (x+4) is a factor.

So P(x) = Ax(x-4)²(x+4)

As it passes through (5,18) so

18 = A.5.(5-4)² . (5+4)

So, A = 18/5 .(1/9)

= 2/5

Therefore, The polynomial is P(x)= 2/5x(x-4)²(x+4)

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Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To calculate Julie's z-score, we need to use the formula:

z = (x - μ) / σ

where:

x is Julie's score on the final (84)

μ is the mean score of the class (75)

σ is the standard deviation of the class (6)

Plugging in the values, we get:

z = (84 - 75) / 6

z = 1.5

Therefore, Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

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