1) CNNBC recently reported that the mean annual cost of auto insurance is 1045 dollars. Assume the standard deviation is 203 dollars, and the cost is normally distributed. You take a simple random sample of 39 auto insurance policies. Round your answers to 4 decimal places.

a. What is the distribution of X? X ~ N

b. What is the distribution of xx? xx ~ N

c. What is the probability that one randomly selected auto insurance is more than $1001?

d. a simple random sample of 39 auto insurance policies, find the probability that the average cost is more than $1001.

e. For part d), is the assumption of normal necessary? Yes or No

2) Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $182,000. Assume the standard deviation is $42,000. Suppose you take a simple random sample of 47 graduates. Round all answers to four decimal places if necessary.

a. What is the distribution of XX? XX ~ N

b. What is the distribution of xx? xx ~ N

c. For a single randomly selected graduate, find the probability that her salary is between $173,511 and $180,874.

d. For a simple random sample of 47 graduates, find the probability that the average salary is between $173,511 and $180,874.

e. For part d), is the assumption of normal necessary? Yes No

3) The average number of miles (in thousands) that a car's tire will function before needing replacement is 69 and the standard deviation is 18. Suppose that 43 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution of X? X ~ N

b. What is the distribution of xx? xx ~ N

c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65.1 and 67.4.

d. For the 43 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65.1 and 67.4.

e. For part d), is the assumption that the distribution is normal necessary? Yes or No

4) The average amount of money spent for lunch per person in the college cafeteria is $6.55 and the standard deviation is $2.33. Suppose that 18 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N

b. What is the distribution of xx? xx ~ N

c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.2762 and $6.9708.

d. For the group of 18 patrons, find the probability that the average lunch cost is between $6.2762 and $6.9708.

e. For part d), is the assumption that the distribution is normal necessary? No or Yes

5) The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 8 mL. Suppose that 47 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N

b. What is the distribution of xx? xx ~ N

c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60 mL and 61.2 mL.

d. For the group of 47 pancake eaters, find the probability that the average amount of syrup is between 60 mL and 61.2 mL.

e. For part d), is the assumption that the distribution is normal necessary? Yes No

6) The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 5 ounces. 15 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N

b. What is the distribution of xx? xx ~ N

c. What is the probability that one randomly selected person drinks between 16.5 and 17.5 ounces of coffee per day?

d. For the 15 people, find the probability that the average coffee consumption is between 16.5 and 17.5 ounces of coffee per day.

e. For part d), is the assumption that the distribution is normal necessary? Yes or No

f. Find the IQR for the average of 15 coffee drinkers.

Q1 = _ounces

Q3 = _ ounces

IQR: _ounces

7) Suppose that the average number of Facebook friends users have is normally distributed with a mean of 127 and a standard deviation of about 47. Assume seven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

a. What is the distribution of xx? xx ~ N

b. For the group of 7, find the probability that the average number of friends is more than 139.

c. Find the first quartile for the average number of Facebook friends.

d. For part b), is the assumption that the distribution is normal necessary? No or Yes