Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205 inches. If 79 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 205.3 inches? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 205

standard deviation = = 1.5

= / n = 1.5 / 79 = 0.1688

P( < 205.3) = P(( - ) / < (205.3 - 205) / 0.1688)

= P(z < 1.7773)

= 0.9622

Probability = 0.9622