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?

Answer 1

31.9 cm differs from mean by 3 standard deviations.

Explanation:

Given:

Mean diameter of the ball = 28 cm

Standard deviation = 1.3 cm

Thus the number of standard deviations by which 31.9 cm ball size differs from the mean ball size is given by the standard normal deviate (Z) given by

`Z=\frac{X-\bar{X}}{\sigma }`

Applying values we get

`Z=(31.9-28)/(1.3 )=3`

Thus 31.9 cm differs from mean by 3 standard deviations.