Question 1

A variable is normally distributed with mean 23 and standard deviation 4. Find each of the following probabilities. Give the answer to 4 decimal places as needed. (If you work with the standard normal table, your answer may be preferrable over the answer shown after your last try.) a) P(x 23) = b) P(x 17) = c) P(17 x 30) = d) P(x 29) = e) P(x 28)

Question 2

Major is conducting market research on the cost of a private helicopter tour. Major has determined that the average cost of a private helicopter tour is $550, and that the distribution of costs is normally distributed with a standard deviation of $82. a. Find the probability that a single randomly selected consumer spends more than $460 on a private helicopter tour.

b. The cost of the middle 70% of private helicopter tours falls between (round to the nearest dollar):

$ ---to $-------

c. The most expensive 7% of private helicopter tours cost at least how much? (round to the nearest dollar)

$---

d. Find the probability that the mean of a sample of 26 private helicopter tour costs will be less than $540.

Question 3

Jayla is conducting market research on the cost of a private helicopter tour. Jayla has determined that the average cost of a private helicopter tour is $590, and that the distribution of costs is normally distributed with a standard deviation of $62. a. Find the probability that a single randomly selected consumer spends less than $640 on a private helicopter tour.

b. The cost of the middle 50% of private helicopter tours falls between (round to the nearest dollar):

$ ---t0 $------

c. The most expensive 17% of private helicopter tours cost at least how much? (round to the nearest dollar)

$---

Question 4

A population of values has an unknown distribution with u=233.6 and q=9.8. You intend to draw a random sample of size n=36. What is the mean of the distribution of sample means? ux= (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? qx= (Please report your answer accurate to 2 decimal places.)

Question 5

Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 2.1 month. 34 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 12.9 and 13.2 months old?

b) For the 34 people, find the probability that the average age that they learned to walk is between 12.9 and 13.2 months old.

c)Find the IQR for the average first time walking age for groups of 34 people. Round to two decimal places.

Q1 =------ months

Q3=--------months

IQR=------months

Question 6 Central Limit Theorem for Sums Suppose random samples of n=32 are collected from an unknown distribution with the properties u=50 and q=2.

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

Question 7

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 N(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? P(X5520)= (Include three decimal places.)
2. Determine the z-score of X=5520 for a sample of 85. z = (Include three decimal places.)

Question 8

A variable is normally distributed with mean 22 and standard deviation 6. Find each of the following probabilities. Give the answer to 4 decimal places as needed. (If you work with the standard normal table, your answer may be preferrable over the answer shown after your last try.) a) P(x 19) = b) P(x 17) = c) P(17 x 29) = d) P(x 27) = e) P(x 24) =

Question 9

Zari is conducting market research on the cost of a private helicopter tour. Zari has determined that the average cost of a private helicopter tour is $600, and that the distribution of costs is normally distributed with a standard deviation of $61. a. Find the probability that a single randomly selected consumer spends more than $650 on a private helicopter tour.

b. The cost of the middle 40% of private helicopter tours falls between (round to the nearest dollar):

$ ---to $--

c. The most expensive 20% of private helicopter tours cost at least how much? (round to the nearest dollar)

$---

d. Find the probability that the mean of a sample of 18 private helicopter tour costs will be less than $590.

Question 10

Heights of 10 year olds: Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Please round your answers to two decimal places. (a) What is the probability that a randomly chosen 10 year old is shorter than 48 inches? (b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches? (c) If the tallest 10% of the class is considered "very tall", what is the height cutoff for "very tall"? inches (d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of 10 year olds cannot go on this ride?

Question 11

Taylor is conducting market research on the cost of a cruise vacation. Taylor has determined that the average cost of a cruise vacation is $3700, and that the distribution of costs is normally distributed with a standard deviation of $400. a. Find the probability that a single randomly selected consumer spends more than $4230 on a cruise vacation.

b. The cost of the middle 30% of cruise vacations falls between (round to the nearest dollar):

$---- to $---

c. The most expensive 14% of cruise vacations cost at least how much? (round to the nearest dollar)

$---

Question 12 Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 136.9 ft and a standard deviation of 6.8 ft. A tree of this type grows in my backyard, and it stands 121.9 feet tall. What percent of these trees is as tall as mine or shorter? (Answer in percent, round percentage to 1 decimal place.) P(X<121.9) = % My neighbor also has a tree of this type growing in her backyard, but hers stands 151.9 feet tall. What percent of these trees are at least as tall as hers? (Answer in percent, round percentage to 1 decimal place.)

P (X >151.9) =%

Question 13

Lewis is conducting market research on the cost of auto insurance. Lewis has determined that the average annual cost of auto insurance is $1045, and that the distribution of costs is normally distributed with a standard deviation of $83. a. Find the probability that a single randomly selected consumer spends less than $965 on auto insurance.

b. The cost of the middle 40% of auto insurance policies falls between (round to the nearest dollar):

$ to $ per year.

c. If a random sample of 50 consumers is selected, what is the probability that the sample average annual cost of their auto insurance policies is between $1042 and $1070?