Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 176 millimeters, and a variance of 100 . If 446 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would be less than 175.35 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 176

standard deviation = = 10

n = 446

= 176

= / n = 10 / 446 = 0.4735

P( < 175.35) = P(( - ) / < (175.35 - 176) / 0.4735)

= P(z < -1.37)

= 0.0853

Probability = 0.0853