If all normal distributions have the same shape, how do they differ?

(a) At what x value does f (x) reach a maximum for a normal distribution N(75, 5)? (b) Does f (x) touch the X-axis at μ 6 3σ?

State the Empirical Rule for a normal distribution (see Chapter 4).

Discuss why you would or would not expect each of the following variables to be normally distributed. Hint: Would you expect a single central mode and tapering tails? Would the distribution be roughly symmetric? Would one tail be longer than the other?

a. Shoe sizes of adult males.

b. Years of higher education of 30-year-old employed women.

c. Days from mailing home utility bills to receipt of payment.

d. Time to process insurance claims for residential fire damage.

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