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A recent study following attrition rates at a major university has shown that 43% of all incoming freshmen do not graduate within 4 years of entrance.

(17) A recent study following attrition rates at a major university has shown that 43% of all incoming freshmen do not graduate within 4 years of entrance. If 200 freshmen are randomly sampled this year and their progress is followed, what is the probability that 100 or less will not graduate within the next 4 years. Verify that the nominal distribution can be used to approximate the binomial distribution in this situation.

Convert the binomial probability P(x < 100) to a normal probability by using the correction for continuity, and then find P(x <= 100).

(18) You are the credit manager for a large corporation and are interested in determining the mean number of business days that lapse between the mailing out of a bill and receipt of payment. Suppose you took a sample of 300 bills and found that that the sample mean time was 23 business days. From past records on payments you have a value for the population standard deviation of 8 days. Assume that the distribution of days between billing and payment is normal. Decide whether the normal distribution or the t-distribution, and then construct the 95% and 99% confidence intervals for the population mean u, number of business days that lapse between the mailing out of a bill and receipt of payment. Which confidence interval is wider, and why?

Solution Summary

This solution provides step by step calculations for converting binomial probability and finding sizes of confidence intervals.

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