# sampling distribution of proportions

The president of Doerman Distributors, Inc., believes that 34% of the firm's orders come from first-time customers. A simple random sample of 120 orders will be used to estimate the proportion of first-time customers

a. What is the probability that the sample proportion will be between .25 and .35 (to 4 decimals)?

Time/CNN voter polls monitored public opinion for the presidential candidates during the 2000 presidential election campaign. One Time/CNN poll conducted by Yankelovich Partners, Inc., used a sample of 589 likely voters (Time, June 26, 2000). Assume the population proportion for a presidential candidate is p = .50. Let be the sample proportion of likely voters favoring the presidential candidate.

a. What is the probability the Time/CNN poll will provide a sample proportion within +/- .04 of the population proportion (to 4 decimals)?

What is the probability the Time/CNN poll will provide a sample proportion within +/- .03 of the population proportion (to 4 decimals)?

c. What is the probability the Time/CNN poll will provide a sample proportion within +/- .02 of the population proportion (to 4 decimals)?

Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the average annual Medicare spending per enrollee was $3267; in 2003, the average annual Medicare spending per enrollee was $6883 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to further investigate the nature of expenditures. Assume the population standard deviation for 2003 was $1900.

What is the probability the sample mean will be greater than $7500 (to 4 decimals)?

If the consulting firm tells you the sample mean for the Medicare enrollees it interviewed was $7500, would you question whether the firm followed correct simple random sampling procedures?

#### Solution Summary

The solution provides step by step method for the calculation of sampling distribution for proportions . Formula for the calculation and Interpretations of the results are also included.