Question

A manufacturer knows that their items have a normally distributed length, with a mean of 16.3 inches, and standard deviation of 4.5 inches.

If 3 items are chosen at random, what is the probability that their mean length is less than 15.1 inches?

Answer 1

Solution :

Given that,

mean = = 16.3

standard deviation = = 4.5

n = 3

= 16.3

= / n = 4.5 3 = 2.5981

P( < 15.1 )

P ( - / ) < ( 15.1 - 16.3 / 2.5981)

P ( z < -1.2 / 2.5981 )

P ( z < -0.46)

= 0.3228

Probability =0.3228