Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 198198 millimeters, and a variance of 100100.

If 228228 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would be greater than 197.12197.12 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 198

standard deviation = = 100=10

n = 228

= 198

= / n = 10/ 228=0.6623

P( >197.12 ) = 1 - P( <197.12 )

= 1 - P[( - ) / < (197.12 -198) /0.6623 ]

= 1 - P(z <-1.33)

Using z table

= 1 - 0.0918

=0.9082

probability=0.9082