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 31.9 cm differ from the mean?

A.) 1
B.) 1.3
C.) 2
D.) 3

Answer 1

Answer: a. 1

Explanation:

Answer 2

Answer: D.) 3

Explanation:

Given: Mean diameter:
`\mu=28\ cm`

Standard deviation:
`\sigma=1.3\ cm`

The required number of standard deviations is given by :-

`z=(X-\mu)/(\sigma)\\\\\Rightarrow\ z=(31.9-28)/(1.3)\\\\\Rightarrow\ z==3`

Hence, a beach ball with a diameter of 31.9 cm is 3 standard deviations differ from the mean.