Question

A manufacturer knows that their items have a normally distributed length, with a mean of 10.9 inches, and standard deviation of 1.2 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?

Answer 1

The probability that their mean length is less than 11.2 inches is 0.5987

Explanation:

Mean = 10.9 inches

Standard deviation = 1.2 inches

We are supposed to find If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches

Formula :
`Z=(x-\mu)/(\sigma)`

We are supposed to find P(x<11.2)

`Z=(11.2-10.9)/(1.2)`

`Z=0.25`

Refer the z table for p value

p value = 0.5987

Hence the probability that their mean length is less than 11.2 inches is 0.5987