Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 178 millimeters, and a standard deviation of 12 millimeters. If 76 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would be greater than 177.44 millimeters? Round your answer to four decimal places.

Answer 1

Given that ,

mean = = 178

standard deviation = = 12

n = 76

=   = 178 and

= / n = 12 / 76 = 1.3765

P( > 177.44) = 1 - P( < 177.44)

= 1 - P(( - ) / < (177.44 - 178) / 1.3765)

= 1 - P(z < -0.41)

= 1 - 0.3409 Using standard normal table.

= 0.6591

Probability = 0.6591