Question1 :A random sample is drawn from a normally distributed population with mean= 17 and standard deviation= 2.1.[You may find it useful to reference thez table.]

a.Are the sampling distribution of the sample mean withn= 25 andn= 48 normally distributed?

multiple choice

• Yes, both the sample means will have a normal distribution.
• No, both the sample means will not have a normal distribution.
• No, only the sample mean withn= 25 will have a normal distribution.
• No, only the sample mean withn= 48 will have a normal distribution.

b.Calculate the probabilities that the sample mean is less than 17.5 for both sample sizes.(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 2: A random sample is drawn from a population with mean= 54 and standard deviation= 4.5.[You may find it useful to reference thez table.]

a.Is the sampling distribution of the sample mean withn= 13 andn= 35 normally distributed?

multiple choice

• Yes, both the sample means will have a normal distribution.
• No, both the sample means will not have a normal distribution.
• No, only the sample mean withn= 13 will have a normal distribution.
• No, only the sample mean withn= 35 will have a normal distribution.

b.Calculate the probability that the sample mean falls between 54 and 56 forn= 35.(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 3: A random sample of sizen= 55 is taken from a population with mean= 10.5 and standard deviation= 2.[You may find it useful to reference thez table.]

a.Calculate the expected value and the standard error for the sampling distribution of the sample mean.(Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard error" to 4 decimal places.)

b.What is the probability that the sample mean is less than 11?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 4: Beer bottles are filled so that they contain an average of 475 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml.[You may find it useful to reference thez table.]

a.What is the probability that a randomly selected bottle will have less than 470 ml of beer?(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

b.What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 470 ml?(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that a randomly selected 12-pack of beer will have a mean amount less than 470 ml?(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 5:

The typical college student graduates with $26,800 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $6,000.[You may find it useful to reference thez table.]

a.What is the probability that the average debt of two recent college graduates is more than $31,000?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

b.What is the probability that the average debt of two recent college graduates is more than $36,000?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 6: Consider a population proportionp= 0.88.

a-1.Calculate the expected value and the standard error ofP

P

withn= 30.(Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.)

a-2.Is it appropriate to use the normal distribution approximation forP

P

?

No

b-1.Calculate the expected value and the standard error ofP

P

withn= 60.(Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.)

Question 7: Consider a population proportionp= 0.25.[You may find it useful to reference thez table.]

a.Calculate the standard error for the sampling distribution of the sample proportion whenn= 15 andn= 63?(Round your final answer to 4 decimal places.)

b.Is the sampling distribution of the sample proportion approximately normalwithn= 15 andn= 63?

c.Calculate the probability that the sample proportion is between 0.23 and 0.25 forn= 63.(Round "z-value" to 2 decimal places and final answer to 4 decimal places.)

Question 8: A random sample of sizen= 200 is taken from a population with a population proportionp= 0.71.(You may find it useful to reference thez table.)

a.Calculate the expected value and the standard error for the sampling distribution of the sample proportion.(Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.)

b.What is the probability that the sample proportion is between 0.70 and 0.80?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

c.What is the probability that the sample proportion is less than 0.70?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 9: A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 50 customers. The dealer will be fined if the number of customers who report favorably is between 29 and 41. The dealership will be dissolved if fewer than 29 customers report favorably. It is known that 71% of the dealer's customers report favorably on satisfaction surveys.[You may find it useful to reference thez table.]

a.What is the probability that the dealer will be fined?(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

b.What is the probability that the dealership will be dissolved?(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 10:While starting salaries have fallen for college graduates in many of the top hiring fields, there is some good news for business undergraduates with concentrations in accounting and finance (Bloomberg Businessweek, July 1, 2010). According to the National Association of Colleges and Employers' Summer 2010 Salary Survey, accounting graduates commanded the second highest salary at $50,402, followed by finance graduates at $49,703. Let the standard deviation for accounting and finance graduates be $6,000 and $10,000, respectively.[You may find it useful to reference thez table.]

a.What is the probability that 100 randomly selected accounting graduates will average more than $52,000 in salary?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

b.What is the probability that 100 randomly selected finance graduates will average more than $52,000 in salary?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 11:Data from the Bureau of Labor Statistics' Consumer Expenditure Survey show that annual expenditures for cellular phone services per consumer unit increased from $210 in 2001 to $608 in 2007. Let the standard deviation of annual cellular expenditure be $48 in 2001 and $132 in 2007.[You may find it useful to reference thez table.]

a.What is the probability that the average annualexpenditure of 100 cellular customers in 2001 exceeded $200?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

b.What is the probability that the average annualexpenditure of 100 cellular customers in 2007 exceeded $600?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Question 12:The weight of people in a small town in Missouri is known to be normally distributed with a mean of 186 pounds and a standard deviation of 29 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3,510 pounds or 18 persons." What is the probability that a random sample of 18 persons will exceed the weight limit of 3,510 pounds?(You may find it useful to reference thez table.Round "z" value to 2 decimal places, and final answer to 4 decimal places.)