Question

A manufacturer knows that their items have a normally distributed length, with a mean of 12.4 inches, and standard deviation of 2.1 inches.

If 21 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?

P(¯x<11.2)=P(x¯<11.2)=

Answer 1

Solution :

Given that ,

mean = = 12.4

standard deviation = = 2.1

= / n = 2.1 / 21 = 0.4583

P( < 11.2) = P(( - ) / < (11.2 - 12.4) / 0.4583)

= P(z < -2.6184)

= 0.0044

P( < 11.2) = 0.0044