Question

The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches. Use the Empirical Rule to determine the interval and contains the middle 68% of the heights.

a) [40,70]

b)[45,70]

c)[50,60]

d)[45,65]

e)[47,63]

d)none of the above

Answer 1

Answer: c)[50,60]

Explanation:

The Empirical rule says that , About 68% of the population lies with the one standard deviation from the mean (For normally distribution).

We are given that , The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches.

Then by Empirical rule, about 68% of the heights of students lies between one standard deviation from mean.

i.e. about 68% of the heights of students lies between
`\text{Mean}\pm\text{Standard deviation}`

i.e. about 68% of the heights of students lies between
`55\pm5`

Here,
`55\pm5=(55-5, 55+5)=(50,60)`

i.e. The required interval that contains the middle 68% of the heights. = [50,60]

Hence, the correct answer is c) (50,60)