Cashier records from the last year show that 60% of all Grayson's Grocery store customers use a previously-obtained Grayson's discount card upon checkout. Management suspects the percentage of actual cardholders is higher because some customers may not use their Grayson's card during every visit They decide to sample random customers who enter the store, and ask them if they have a Grayson's card.

Suppose they solicit 400 customers one day, and find that 250 of them have a Grayson's card. Assume that 60% of all Grayson's customers have a discount card, what is the probability of getting a sample proportion of at least 250 / 400=0.625?

Solution Preview

In this problem, we shall apply normal approximation to binomial distribution.

Sample Proportion,p =0.6
q=1-p=0.4
Sample ...

Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problem. Calculations have been shown both in text. The solution provides students with a clear perspective of the underlying concepts.

Roper ASW conducted a survey to learn about American adults' attitudes toward money and happiness. 56% of the respondents said they balance their checkbook at least once a month.
a. Suppose a sample of 400 American adults were taken. Show the sampling distribution of the proportion of adults who balance their checkbook at le

SEE ATTACHED FILE - Error of the SampleProportion
It has been reported that 42.6% of U.S. workers employed as purchasing managers are females. In a simple random sample of U.S. purchasing managers, 70 out of the 200 are females. Given this information:
a. What is the population proportion, π?
b. What is the sample

Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be called millionaires. However, a survey in the year 2000 found that 30% of Microsoft's 31,000 employees were millionaires. If random samples of 100 Microsoft employees had taken that year, what's the probability that the sampleproportion

According to accountemps inc. 48% of all executives believe that employees are most productive on Tuesdays. a random sample of 200 executives is taken for a study.
a. what is the shape, mean, and standard deviation of the sampling distribution of the sampleproportion for samples of 200?
b. what is the probability that the

A poll of 1,250 investors conducted, assume that 50% of the investors found the market less attractive to the prior years. P=.5, find the probability that the sampleproportion obtained from the sample of 1,250 investors would be:
A. within 4% points of the population, that is P(.46<^p<.54).
B. within 2% points of the pop

In an online survey of 4,001 respondents, 8% were classified as productivity enhancers who are comfortable with technology and use the Internet for its practical value (data extracted from M. Himowitz, "How to Tell What Kind of Tech User You Are," Newsday, May 27, 2007, p F6). Suppose you select a sample of 400 students at your

1. The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky. Use this price as the population mean, and assume the population standard deviation is $0.20.
a. What is the probability that the mean price for a sample of 30 service stations is within $0.03 of the population mean?

The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25
a. Show the sampling distribution of p, the proportion of late flights in a sample of 1000 flights.

The president of Doerman Distributors, Inc., believes that 26% of the firm's orders come from first-time customers. A simple random sample of 80 orders will be used to estimate the proportion of first-time customers.
Assume that the president is correct and p = 0.26. What is the sampling distribution for this study?
Select