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

Step-by-step explanation:

We have been given that a shipment of beach balls with a mean diameter of 28 cm and a standard deviation of 1.3 cm is normally distributed.  

Since z-score represents that a raw score is how many standard deviation above or below mean.

To solve our given problem we will use z-score formula.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{z-score}$,

$x=\text{Raw score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$.

Upon substituting our given values in z-score formula we will get,

$z=\frac{26.7-28}{1.3}$

$z=\frac{-1.3}{1.3}$

$z=-1$

Therefore, a beach ball with a diameter of 26.7 cm differs -1 standard deviation from the mean and option A is the correct choice.