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

Answer:

31.9 cm differs from mean by 3 standard deviations.

Step-by-step 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

$Z=\frac{31.9-28}{1.3 }=3$

Thus 31.9 cm differs from mean by 3 standard deviations.