In a sample of 1000 gas stations across the USA, the price of regular gasoline at the pump was $3.429 per gallon and the standard deviation was $0.162 per gallon. A random sample of size 100 gas stations was drawn from that population. What is the probability that the mean price per gallon is less than $3.399? Round your answer to 4 decimal places.
Suppose you are a researcher for a consumer’s advocate magazine. You want to find a sample of cars whose owners have paid for rebuilt transmissions. So, you randomly select a sample of 40 replacement costs and find the mean to be $2,585. The sample standard deviation is $465. Calculate the 95% confidence interval for the population mean replacement cost. Interpret your results.
Suppose you want to estimate the mean weight loss of people one year after using the Atkins weight loss program. How many people on that program must be surveyed if you want to be 95% confident that the sample mean weight loss is within 0.25 pounds of the population mean? Assume that the population standard deviation is known to be 10.6 pounds based on previous research.
In a recent study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were later dropped or dismissed based on data from a reputable insurance organization for physicians. Use that information to construct a 99% confidence interval estimate of the population proportion of medical malpractice lawsuits that are dropped or dismissed.