Answer:
The number of students reporting readings between 87 g and 89 g is 61
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 88g
Standard deviation = 1g
Percentage of students reporting readings between 87 g and 89 g
87 = 88-1
So 87 is one standard deviation below the mean.
89 = 88+1
So 89 is one standard deviation above the mean.
By the Empirical Rule, 68% of students are reporting readings between 87 g and 89 g.
Out of 90 students:
0.68*90 = 61.2
Rounding to the nearest whole number:
The number of students reporting readings between 87 g and 89 g is 61
Please help! Correct answer only, please! Consider the matrix shown below: What are the dimensions of A. A. 3 X 4 B. 4 X 3 C. 12 D. A and B
Answer: A) 3 x 4
Step-by-step explanation:
The dimensions of a matrix are ROWS x COLUMNS.
The given matrix has 3 rows and 4 columns,
therefore the dimensions are: 3 x 4
Provide three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation based on the variables involved. Explain why?
Answer:
Step-by-step explanation:
You are rolling two dice. When the two numbers (1-6) come up, you multiply the numbers
together. What is the probability of getting a product that is NOT divisible by 2?*
Answer:
1/4 probability of getting a product that isn't divisible by 2.
Step-by-step explanation:
These are all the possible outcomes
1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6
1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12
1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18
1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24
1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25 6 x 5 = 30
1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36
All of the outcomes that aren't divisible by 2 are in bold
There are 9 out of 36 possible outcomes that aren't divisible by 2
9/36 = 1/4
Suppose f '' is continuous on (−[infinity], [infinity]). (a) If f '(−5) = 0 and f ''(−5) = −1, what can you say about f ? At x = −5, f has a local maximum. At x = −5, f has a local minimum. At x = −5, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = −5. (b) If f '(1) = 0 and f ''(1) = 0, what can you say about f ? At x = 1, f has a local maximum. At x = 1, f has a local minimum. At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1.
Answer:
Step-by-step explanation:
a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.
The second derivative helps determining the concave up/down.
At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.
Hence f'(-5) = 0 shows f gets maximum at -5.
b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.
Using concepts of critical points, it is found that:
a) At x = −5, f has a local maximum.
b) At x = 1, f has neither a maximum nor a minimum.
-----------------------
A critical value of a function f(x) is a value of [tex]x^{\ast}[/tex] for which: [tex]f^{\prime}(x^{\ast}) = 0[/tex].
The second derivative test is also applied:
If [tex]f^{\prime\prime}(x^{\ast}) > 0[/tex], [tex]x^{\ast}[/tex] is a minimum point.If [tex]f^{\prime\prime}(x^{\ast}) < 0[/tex], [tex]x^{\ast}[/tex] is a maximum point.If [tex]f^{\prime\prime}(x^{\ast}) = 0[/tex], [tex]x^{\ast}[/tex] is neither a maximum nor a minimum point.Item a:
[tex]f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1[/tex], thus, a maximum point, and the correct option is:At x = −5, f has a local maximum.
Item b:
[tex]f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0[/tex], thus, neither a maximum nor a minimum point, and the correct option is:At x = 1, f has neither a maximum nor a minimum.
A similar problem is given at https://brainly.com/question/16944025
Please answer this correctly
Answer:
1 flowers
Step-by-step explanation:
The graph shows that only one flower received more than [tex]4\frac{1}{2}[/tex] cups of water and that is the plant that received 5 cups of water.
1 flower
Step-by-step explanation:
the question asks for flowers above the 4 1/2 mark and only 1 flower is there.
find the mean of the following numbers 7,21,2,17,3,13,7,4,9
Answer:
9.222222222
Step-by-step explanation:
7+21+2+17+3+13+7+4+9 = 83
7+21+2+17+3+13+7+4+9 = 83 83÷9 = 9.222222222
_____________________________
Hey!!
Solution,
Given data=7,21,2,17,3,13,7,4,9
summation FX= 83
N(total no. of items)=9
Now,
Mean=summation FX/N
= 83/9
=9.23
So the answer is 9.23
__________________________
The total claim amount for a health insurance policy follows a distribution with density function 1 ( /1000) ( ) 1000 x fx e− = , x > 0. The premium for the policy is set at the expected total claim amount plus 100. If 100 policies are sold, calculate the approximate probability that the insurance company will have claims exceeding the premiums collected.
Answer:
the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Step-by-step explanation:
The probability of the density function of the total claim amount for the health insurance policy is given as :
[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]
Thus, the expected total claim amount [tex]\mu[/tex] = 1000
The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]
However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100
To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :
P(X > 1100 n )
where n = numbers of premium sold
[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]
[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]
[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
There are 15 marbles in a bag; 10 are blue, 4 are red and 1 is green. Marbles are drawn and NOT replaced 8 times, with the number of red marbles being recorded. What is the probability of getting exactly 3 red marbles? (Write as a percentage, correct to two decimals. eg: 12.34%)
Answer: There is a 0.88% chance of pulling three red marbles in a row.
Step-by-step explanation:
First pull = 4/15 (26.67%)
second pull = 3/14 (21.43%)
Third pull = 2/13 (15.38%)
You need to multiply these three fractions to get the probability of pulling three reds in a row, doing that will get you 4/455 or 0.88%
List the important features for the graph of a quadratic function.
Answer:
VertexMinimum PointMaximum PointRootsAxis of SymmetryStep-by-step explanation:
The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.
The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.
If possible, please mark brainliest
The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The important features for the graph of a quadratic function will be
The parabola is symmetric about the line which is passing through focus.
The quadratic function can be expressed in the form of vertex form.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
#SPJ2
a cereal box is an example of a
Answer: recantagle
Step-by-step explanation:
A retail company estimates that if it spends x thousands of dollars on advertising during the year, it will realize a profit of P ( x ) dollars, where P ( x ) = − 0.5 x 2 + 120 x + 2000 , where 0 ≤ x ≤ 187 . a . What is the company's marginal profit at the $ 100000 and $ 140000 advertising levels? P ' ( 100 ) = P ' ( 140 ) = b . What advertising expenditure would you recommend to this company? $
Answer:
Step-by-step explanation:
If the profit realized by the company is modelled by the equation
P (x) = −0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0
dP/dx = -x+120
P'(x) = -x+120
Company's marginal profit at the $100,000 advertising level will be expressed as;
P '(100) = -100+120
P'(100) = 20
Marginal profit at the $100,000 advertising level is $20,000
Company's marginal profit at the $140,000 advertising level will be expressed as;
P '(140) = -140+120
P'(140) = -20
Marginal profit at the $140,000 advertising level is $-20,000
Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.
Let the velocity of a particle be given by v(t) = 2t+a.(a) Find the number a such that the average value of v(t) on the interval [0,1] is -2.(b) Using v(t) from part (a), find the distance traveled by the particle during the time period from [0,4].
Answer:
The velocity is v(t) = 2*t + a
a) we want to find the average velocity betwen t = 0 and t = 1.
We can do this as:
Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a
b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.
For this we can see the integral:
[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
The cottage inside the pen is a shape of a cylinder.
Answer:
Cylinder
As u can see the shape it's like a cylinder
Employees at a company produced refrigerators on three shifts. Each shift recorded their quality stats below. A unit was considered defective if it at least one part was assembled wrong or was missing. Management believes that quality depends on the the shift it was produced. Test the claim that shifts are independent of quality using chi-square at alpha = 0.05. SHOW YOUR WORK
Answer:
Step-by-step explanation:
Hello!
So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.
Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.
The hypotheses are:
H₀: The variables are independent.
H₁: The variables are not independent.
α: 0.05
[tex]X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}[/tex]
r= total number of rows
c= total number of columns
i= 1, 2 (categories in rows)
j=1, 2, 3 (categories in columns)
To calculate the statistic you have to calculate the expected frequencies for each category:
[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]
[tex]O_{i.}[/tex] Represents the marginal value of the i-row
[tex]O_{.j}[/tex] Represents the marginal value of the j-column
[tex]E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34[/tex]
Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:
[tex]X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991[/tex]
Decision rule:
If [tex]X^2_{H_0}[/tex] ≥ 5.991, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 5.991, do not reject the null hypothesis.
The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.
At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.
I hope this helps!
Does a point have a one dimension length
Answer:
No.
Step-by-step explanation:
A point has no length, height or depth. It only has position.
A line has one dimensional length.
I will give brainiest to the first to answer. The what
of the following set of data is 5.
13, 7, 9, 5, 2, 3, 5, 4, 10, 12
Answer:
it is the mode.
Step-by-step explanation:
i. e 5 is the most occuring number in the set of data listed above
What is the value of X?
Answer:
x = 41 ft
Step-by-step explanation:
35(35+23) = 29(29+x)
2030 = 29(29+x)
70 = 29 + x
x = 41 ft
a line has a slope of -3/4 and passes through the point (-5, 4). what is the equation of the line?
Answer:
y = -3/4x-1/4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = -3/4x +b
We have a point (-5,4)
4 = -3/4 (-5) +b
Changing to a common denominator
16/4 = 15/4 +b
subtracting 15/4 from each side
16/4-15/4 = -15/4 +15/4 +b
1/4 = b
y = -3/4x-1/4
Answer:
book
Step-by-step explanation:
kmgktn
Write a simplified expression for the area of the rectangle below
Answer:
12x+40
Step-by-step explanation:
A=l*w
A=20(3/5x+2)
A=4*3x+20*2
A=12x+40
Answer:
[tex] = 12x + 40[/tex]
Step-by-step explanation:
[tex]area = l \times b \\ = 20 \times (\frac{3}{5} x + 2) \\ = \frac{60x}{5} + 40 \\ = 12x + 40[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A sports car manufacturer paints its cars silver, white, black, and red in the following proportions: ?
Color: Silver White Black Red
Proportion: .2 .3 .1 .4
We know that 40% of these cars are manufactured with tan leather upholstery while the remaining 60% are manufactured with gray leather.
A. Assuming that the choice of exterior color and leather color are independent, what is the probability that a randomly selected sports car from this manufacturer will be white with gray upholstery?
B. Assuming that we know the car has tan upholstery, what is the probability that the car is either silver or white?
Answer:
A. The probability that a randomly selected sports car from this manufacturer will be white with gray upholstery is P=0.12.
B. Assuming that we know the car has tan upholstery, the probability that the car is either silver or white is P=0.50.
Step-by-step explanation:
We first start by stating that the events "exterior color" and "leather color" are independent, so the probability of the outcomes of each event is not affected by the outcomes of the other event.
A. The probability of having a car that is white (W) with gray upholstery (G) is equal to the probability of having a car that is white multiplied by the probability of having a car with gray leather upholstery. Mathematically, this is:
[tex]P(\text{W\&G})=P(W)\cdot P(G)=0.3\cdot 0.4=0.12[/tex]
B. As the events are independent, the probability of having a silver or white car, given that the car has tan upholstery, is the same as the probabiltiy of having a silver or white car:
[tex]P(S\,or\,W | T)=P(S\,or\,W)=P(S)+P(W)=0.20+0.30=0.50[/tex]
Please help me with this question!!!!
Answer:
-3i +-12j
Step-by-step explanation:
P2 -P1 = (-1-2, -6-6) = (-3, -12)
In terms of unit vectors i and j, this is -3i -12j.
Age (years) Population Under 15 2600 15 - 64 16000 Over 64 4000 Calculate the child dependency ratio from the chart above. Round to 3 decimals places.
Answer:
16.25%
=0.163 (correct to 3 decimal places)
Step-by-step explanation:
The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]
From the given table:
Population Under 15 years = 2600
Population of the working class (between 15-64) = 16000
Therefore:
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]
=0.163 (correct to 3 decimal places)
5/2 = 11/x
What is x
Answer:
X=22/5
Step-by-step explanation:
By cross multiplication
5/2 =11/x
5x = 2(11)
5x =22
X=22/5
Hope this helps..
Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate? Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of
return of 6%? Explain.
Answer:
The simple interest rate is 5%.
This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?
We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.
[tex]E = P*I*t[/tex]
[tex]630 = 4200*I*3[/tex]
[tex]I = \frac{630}{4200*3}[/tex]
[tex]I = 0.05[/tex]
The simple interest rate is 5%.
Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of return of 6%?
We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]
So
[tex]E = P*I*t[/tex]
[tex]E = 4200*0.06*4[/tex]
[tex]E = 1008[/tex]
[tex]T = E + P = 4200 + 1008 = 5208[/tex]
This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.
In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit
Answer:
The expected value of profit is -$0.65.
Step-by-step explanation:
The rules of the lottery are as follows:
You pay $1 and pick a number from 000 to 999.If your number comes up, you win $350, which is a profit of $349.If you lose, you lose $1.The probability of winning is, P (W) = 0.001.
Then the probability of losing will be,
P (L) = 1 - P (W)
= 1 - 0.001
= 0.999
Let the random variable X represent the amount of profit.
The probability distribution table of the lottery result is as follows:
Result X P (X)
Win +349 0.001
Lose -1 0.999
The formula to compute the expected value of X is:
[tex]E(X)=\sum X\cdot P(X)[/tex]
Compute the expected value of profit as follows:
[tex]E(X)=\sum X\cdot P(X)[/tex]
[tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]
Thus, the expected value of profit is -$0.65.
Rectangle WXYZ was dilated to create W'X'Y'Z'. Point G is the center of dilation. Rectangle W X Y Z was dilated to create smaller rectangle W prime X prime Y prime Z prime. The length of G Z prime is 1.5. The length of Z prime Z is 7.5. Side W X is 3 units and side X Y is 6 units. What is W'X'? 0.5 units 1.2 units 1.5 units 1.8 units
Answer:
0.5 units
Step-by-step explanation:
The dilation factor is ...
(GZ')/(GZ) = (GZ')/(GZ' +Z'Z) = 1.5/(1.5 +7.5) = 1/6
Side WX is 3 units, so side W'X' is (1/6)(3 units) = 1/2 units
W'X' is 0.5 units.
Answer:
It is .5 on edge
Step-by-step explanation:
I took the test
Drivers who are members of the teamsters Union earn an average of $17.15 per hour (U.S. News & World Report). Assume that available data indicate wages are normally distributed with a standard deviation of $2.25. 1) What is the probability that wages are between $15.00 and $20.00 per hours?
Answer:
[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]
And we can find the probability with this difference and using the normal standard table:
[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]
Step-by-step explanation:
Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:
[tex]X \sim N(17.15,2.25)[/tex]
Where [tex]\mu=17.15[/tex] and [tex]\sigma=2.25[/tex]
We want to find this probability:
[tex]P(15<X<20)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we have:
[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]
And we can find the probability with this difference and using the normal standard table:
[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]
Math Activity #1
The number of the day is 1,853,604,297.
Write this number in word form:
If a random sample of 53 students was asked for the number of semester hours they are taking this semester. The sample standard deviation was found to be s = 4.7 semester hours. How many more students should be included in the sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean for all students at this college?
Answer:
94 more students should be included in the sample.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?
We need to survey n students.
n is found when M = 1.
We have that [tex]\sigma = 4.7[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 2.575*\frac{4.7}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 2.575*4.7[/tex]
[tex](\sqrt{n})^{2} = (2.575*4.7)^{2}[/tex]
[tex]n = 146.47[/tex]
Rounding up
147 students need to be surveyed.
How many more students should be included...?
53 have already been surveyed
147 - 53 = 94
94 more students should be included in the sample.
A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building?
(Hint: Draw a picture and Set up a proportion)
The building height is 32 feet.
Let us consider that building height is x feet.
From attached diagram shown below,
Two triangles are formed.
Apply law of similarity of triangles.
Corresponding sides are in equal proportion.
[tex]\frac{x}{24}=\frac{12}{9} \\\\9x=12*24\\\\x=\frac{12*24}{9}=32 feet[/tex]
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