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