The Standard and Poor’s (S&P) 500 is a group of 500 large companies traded on the New York Stock Exchange.

Following are prices, in dollars, for a random sample of ten stocks on a recent day.

Assume the population standard deviation is σ = 50.

a. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.

b. Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal?

c. If appropriate, construct a 95% confidence interval for the mean price for all S&P 500 stocks on this day. If not appropriate, explain why not.

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84.86 8.11 74.23 35.25 13.19 53.55 84.25 201.94 24.68 53.47