Question

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 11.5 inches, and standard deviation of 3.2 inches.

If 31 items are chosen at random, what is the probability that their mean length is greater than 10.4 inches?

Please do it step by step thanks

Answer 1

Solution :

Given that ,

= 11.5

= 3.2

A sample of size n = 31 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 11.5

SD =    = 3.2/​31  =  0.57473696

Find P( > 10.4)

= P[( - )/ >  (10.4 - )/]

= P[ ( - )/ > (10.4 - 11.5)/0.57473696 ]

= P[Z > -1.914]

= 1 - P[Z < -1.914]

= 1 - 0.0278 ..... ( use z table)

= 0.9722

P( > 10.4) = 0.9722