Chapter 15.12, Problem 3E

In Exercises 3–6, use the frequency distribution to find a. the mean and b. the sample standard deviation. c. Does the data form a normal distribution? Remember: If the data fall within 2% of the empirical rule of 68%, 95%, and 99.7% for one, two, or three standard deviations, respectively, they form a normal distribution.

Interval	Midpoint $x$	Frequency $f$
41.5-48.5		10
48.5-55.5		50
55.5-62.5		200
62.5-69.5		188
69.5-76.5		40
76.5-83.5		20