Question 1

A population of values has a normal distribution with =218.4 and =44.9. You intend to draw a random sample of size =98. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is greater than 215.7. P(X > 215.7) = Find the probability that a sample of size =98 is randomly selected with a mean greater than 215.7. P( > 215.7) =

Question 2

A population of values has an unknown distribution with =219.5 and =7.9. You intend to draw a random sample of size =73. hat is the mean of the distribution of sample means? = (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? = (Please report your answer accurate to 2 decimal places.)

Question 3

A population of values has a normal distribution with =194.3 and =37.4. You intend to draw a random sample of size =183. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is between 188.5 and 195.4. P(188.5 < X < 195.4) = Find the probability that a sample of size =183 is randomly selected with a mean between 188.5 and 195.4. P(188.5 < < 195.4) =

Question 4

The average production cost for major movies is 58 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 42 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

1. For a single randomly selected movie, find the probability that this movie's production cost is between 60 and 64 million dollars.
2. For the group of 42 movies, find the probability that the average production cost is between 60 and 64 million dollars.
3. For part b, is the assumption of a normal distribution necessary? Yes or No

Question 5

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 134 and a standard deviation of about 51. Assume forty-eight individuals are randomly chosen. Answer the following questions.

a. For the group of 48, find the probability that the average number of friends is less than 138. Round your answer to 4 decimal places. b. Find the third quartile for the average number of Facebook friends. Round your answer to 3 decimal places. c. For part a, is the assumption that the distribution is normal necessary? No or Yes

Question 6

Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 2.2 month. 33 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.

a) What is the probability that one randomly selected person learned to walk when the person was between 12.8 and 13.3 months old?

b) For the 33 people, find the probability that the average age that they learned to walk is between 12.8 and 13.3 months old.

c)Find the IQR for the average first time walking age og groups of 33 people. Round to two decimal places. Q1 =-- months

Q3 =--- months

IQR=---- months

Question 7

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.9 ppm and standard deviation 1.8 ppm. 14 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

1. What is the probability that one randomly selected city's waterway will have less than 9.2 ppm pollutants?
2. For the 14 cities, find the probability that the average amount of pollutants is less than 9.2 ppm.
3. For part b, is the assumption that the distribution is normal necessary? NoYes
4. Find the IQR for the average of 14 cities. Round to two decimal places. Q1 = ppm Q3 = ppm IQR: ppm

Question 8

Central Limit Theorem for Sums Suppose random samples of =37 are collected from an unknown distribution with the properties =47 and =4.

1. Determine the mean of .
2. Determine the standard deviation of . (Include four decimal places.)

Question 9

Application of The Central Limit Theorem for Sums 100 North Main Street is the tallest building in Winston-Salem, NC standing at 460ft tall (5520inches). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of Iowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator)

1. Given that the heights of American women follow the distribution (65,3.5), what is the probability of that a random sample of 85 women, stacked head-to-foot, would be at least as tall as 100 North Main Street? (5520)= (Include three decimal places.)

Question 10

Suppose you have an apple orchard, and the data of previous years' yield per tree is normally distributed with a mean of 256.8 apples with a standard deviation of 30.4 apples.

a)Calculate the probability (rounded to three decimal places) that a randomly selected tree will yield a number of apples between (260 and 280)

b)The probability that the between 260 and 280 apples will yield approximately what?

c)The IQR for this data set rounded to the nearest whole number is?

You may find this web calculator helpful: Calculating the Probability from Given Data Values - Normal Distribution