After 1964, quarters were manufactured so that their weights were normally distributed with a mean of 5.67 g and a standard deviation of 0.06 g. Answer the following questions by hand and using the tables in the back of the book.
a) What percent of quarters weigh more than 5.58 g?
b) Some vending machines are designed so that you can adjust he weights of the quarters that are accepted. If many counterfeit coins are found, you can narrow the range of acceptable weights with the effect that most counterfeit coins are rejected along with some legitimate quarters. If you adjust the vending machine to accept weights between 5.62 g and 5.70 g, what percentage of legal quarters are rejected?
c) Of 7500 quarters, how many would we expect to be unacceptable?
d) By hand and using the normal tables in the back of the book, find the Inter Quartile Range, the range for the middle 50% of the weights of quarters. Check your answer using Excel - Click on the Insert Function fx button on the toolbar -Select NORM.INV in the Select a Function box
e) Based on the accepted weight range from b), and your results from c), and d), do you think the vending machines accept weight range should be changed? Explain.