Question

1)A manufacturer knows that their items have a normally distributed length, with a mean of 13.8 inches, and standard deviation of 3.7 inches.

If 9 items are chosen at random, what is the probability that their mean length is less than 12.5 inches?

Answer 1

Solution :

Given that ,

mean = = 13.8

standard deviation = = 3.7

= / n = 3.7 / 9 = 1.2333

P( < 12.5) = P(( - ) / < (12.5 - 13.8) / 1.2333)   

P(z < -1.05)

0.1469

Probability = 0.1469