Question

question 5 of 10
suppose the heights of the members of a population follow a normal
distribution. if the mean height of the population is 68 inches and the
standard deviation is 4 inches, 99.7% of the population will have a height
within which of the following ranges?

a. 60 inches to 76 inches

b. 56 inches to 80 inches

c. 52 inches to 84 inches

d. 64 inches to 72 inches

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule states that for a normal distribution, approximately 99.7% of the data lies within 3 standard deviations of the mean.

Step2: Calculate the lower and upper bounds

Given mean \(\mu = 68\) inches and standard deviation \(\sigma=4\) inches.
The lower bound is \(\mu - 3\sigma\), so \(68-3\times4=68 - 12=56\) inches.
The upper bound is \(\mu + 3\sigma\), so \(68+3\times4=68 + 12 = 80\) inches.

Answer:

B. 56 inches to 80 inches