Question

question 9 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, 68% of the population will have a height within
which of the following ranges?

a. 52 inches to 84 inches

b. 56 inches to 80 inches

c. 64 inches to 72 inches

d. 60 inches to 76 inches

Explanation:

Step1: Recall the empirical rule for normal distributions

In a normal distribution, approximately 68% of the data lies within 1 standard deviation ($\sigma$) of the mean ($\mu$). The formula for this range is $\mu - \sigma$ to $\mu + \sigma$.

Step2: Identify the mean and standard deviation

Given $\mu = 68$ inches and $\sigma = 4$ inches.

Step3: Calculate the lower and upper bounds

Lower bound: $\mu - \sigma = 68 - 4 = 64$ inches.
Upper bound: $\mu + \sigma = 68 + 4 = 72$ inches.

Answer:

C. 64 inches to 72 inches