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? 1 1.3 2 3

Answer 1

Given:
μ = 28 cm, population mean
σ = 1.3 cm, population standard deviation

Let x = value of a beach ball
Within 1σ from the mean, x = 28 + 1.3 = 29.3 cm
Within 2σ from the mean, x = 28 + 2*1.3 = 30.6 cm
Within 3σ from the mean, x = 28 + 3*1.3 = 31.9 cm

Answer: 3
A beach ball with 31.9 cm diameter differs by 3 standard deviations from the mean.