Question

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 6.256.25 and a mean diameter of 206206 inches. If 9090 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.30.3 inches

Answer 1

Explanation:

mean diameter = 206

variance = 6.25

standard deviation = √ variance

σ = √ 6.25 = 2.5

sample size n = 90

z = deviation from mean / (σ / √n)

= 0.3 / (2.5/ √90)

= .3 / .2635

= 1.1385

P value from the table = (.87 - .5 ) x 2

= .37 x 2 .

or 74 % .