Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 151 millimeters and a variance of 64.

If 116 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would be greater than 151.81 millimeters? Round your answer to four decimal places.

Answer 1

solution

mean =   = 151

standard deviation = = 64=8

n = 116

= 151

=  / n = 8/ 116=0.7428

P( >151.81 ) =1- P( <151.81 )

= 1-P[( - ) / < (151.81 -151) / 0.7428]

=1- P(z < 1.09)

Using z table  

=1- 0.8621

=0.1379

probability= 0.1379