Question

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 6.25 and a mean diameter of 206 inches.

If 90 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 less than 0.3 inches? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 206

standard deviation = = 6.25 = 2.5

n = 90

=   = 206

= / n = 2.5 / 90 =0.264

206  ± 0.3 = 205.7, 206.3

P(205.7 < < 206.3)  

= P[(205.7 - 206) / 0.264 < ( - ) / < (206.3 - 206 ) / 0.264)]

= P( -1.14 < Z < 1.14 )

= P(Z < 1.14) - P(Z < -1.14)

Using z table,  

= 0.8729 - 0.1271

= 0.7458