Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 164 millimeters, and a variance of 121.

If 287 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would be less than 164.56 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 164

standard deviation = = 121=11

n = 287

= 164

=  / n = 11/ 287=0.6493

P( <164.56 ) = P[( - ) / < (164.56-164) / 0.6493]

= P(z <0.86 )

Using z table  

=0.8051   

probability=0.8051