Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 194 millimeters, and a variance of 121 . If 339 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 less than 0.95 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 194

standard deviation = = 11

n = 339

=   = 194

= / n = 11 / 339 = 0.5974

P(193.05 < < 194.95) = P((193.05 - 194) /0.5974 <( - ) / < (1940.95 - 194) / 0.5974))

= P(-1.59 < Z < 1.59)

= P(Z < 1.59) - P(Z < -1.59) Using z table,

= 0.9441 - 0.0559

= 0.8882

The probability that the mean length of the sample rods would differ from the population mean by less than 0.95 millimeters is 0.8882.