Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 170 millimeters, and a standard deviation of 10 millimeters. If 299 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.7 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 170

standard deviation = = 10

= / n = 10 / 299 = 0.5783

= 1 - P[(-0.7) /0.5783 < ( - ) / < (0.7) / 0.5783)]

= 1 - P(-1.21 < Z < 1.21)

= 1 - P(Z < 1.21) - P(Z < -1.21)

= 1 - P(0.8869 - 0.1131)

= 1 - 0.7738

= 0.2262

Probability = 0.2262