Question

A shipment of beach balls with a mean diameter of 28 cm and a standard deviation of 1.3 cm is normally distributed. By how many standard deviations does a beach ball with a diameter of 26.7 cm differ from the mean?

a. 1

b. 1.3

c. 2

d. 3

Answer 1

Answer: a. 1

Explanation:

Given : Population mean :
`\mu=28\ cm`

Standard deviation :
`\sigma=1.3\ cm`

Let n be the number of times a beach ball with a diameter of 26.7 cm differ from the mean.

Then, we have

`28-n(1.3)=26.7\\\\\Rightarrow\ 1.3n=28-26.7\\\\\Rightarrow\ 1.3 n=1.3\\\\\Rightarrow\ n=1`

Hence, a beach ball with a diameter of 26.7 cm is 1 standard deviation differ from the mean.