A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of$20. Is it likely that the next 50 Sunday customers will spend an average of at least $40? Explain.

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of 32 dollars and a standard deviation of 20 dollars.$\newline$ Suppose the store in Exercise 56 had 312 customers this Sunday.$\newline$ Estimate the probability that the store's revenues were at least 10,000 dollars.

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of 28 dollars and a standard deviation of 20 dollars.

Is it likely that the next 60 Sunday customers will spend an average of at least 34 dollarsExplain.

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of 28 dollars and a standard deviation of 20 dollars.

Explain why you cannot determine the probability that the next Sunday customer will spend at least 34 dollars.

You roll a die. If it comes up a 6, you win $100. If not, you get to roll again. If you get a 6 the second time, you win$50. If not, you lose. Find the expected amount you'll win.

Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Assume a company wants to test the response to a new flyer and sends it to 1000 people randomly chosen from their mailing list of over 200,000 people. They get orders from 123 of the recipients.

d) The company must decide whether to now do a mass mailing. The mailing won't be cost-effective unless it produces at least a $5 \%$ return. What does your confidence interval suggest? Describe.

A grocery store 's receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of$20. a) Explain why you cannot determine the probability that the next Sunday customer will spend at least $40. b) Can you estimate the probability that the next 10 Sunday customers will spend an average of at least$40? Explain. c) Is it likely that the next 50 Sunday customers will spend an average of at least $40? Explain.

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of 32 dollars and a standard deviation of 20 dollars.$\newline$ Suppose the store in Exercise 56 had 312 customers this Sunday.$\newline$ If, on a typical Sunday, the store serves 312 customers, how much does the store take in on the worst $10\%$ of such days?

A survey finds that a 95% confidence interval for the mean salary of a police patrol officer in Fresno, California, in 2016 is $52,516 to$53,509. A student is surprised that so few police officers make more than $53,500. Explain what is wrong with the student's interpretation.

A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 35 pounds with a standard deviation of 2 pounds. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 16 salmon, and to discount outlet stores in pallets of 100 salmon. To forecast costs, the shipping department needs to estimate the standard deviation of the mean weight of the salmon in each type of shipment Find the standard deviations of the mean weight of the salmon in each type of shipment.

Direct mail advertisers send solicitations (a.k.a. "junk mail") to thousands of potential customers in the hope that some will buy the company's product. The acceptance rate is usually quite low. Suppose a company wants to test the response to a new flyer, and sends it to 1000 people randomly selected from their mailing list of over 200,000 people. They get orders from 123 of the recipients. Explain what this interval means.

Suppose the store in the earlier exercise had 312 customers this Sunday.

a) Estimate the probability that the store's revenues were at least $10,000.

b) If, on a typical Sunday, the store serves 312 customers, how much does the store take in on the worst 10% of such days?

The automatic character recognition device discussed in the previous exercise successfully reads about $85 \%$ of handwritten credit card applications. In the previous exercise, you looked at the histograms displaying distributions of sample proportions from 1000 simulated samples of size $20,50,75$, and 100 . The sample statistics from each simulation were as follows:

d) What does the Success/Failure Condition say about the choice you made in part c?

The automatic character recognition device discussed in the previous exercise successfully reads about $85 \%$ of handwritten credit card applications. In the previous exercise, you looked at the histograms displaying distributions of sample proportions from 1000 simulated samples of size $20,50,75$, and 100 . The sample statistics from each simulation were as follows:

c) At what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?