A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77 and a sample standard deviation of $15.

a)Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

b)Explain, in context, what the interval you found tells you.

c)What sample size would be necessary to achieve a margin of error of $2? Assume a confidence level of 95%.

d)Three years ago the mean price charged for a trade of 100 shares at $50 per share was $39.25. Has the price dropped significantly? Justify.