Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.3 and a mean diameter of 208 inches.

If 60 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be greater than 208.1 inches? Round your answer to four decimal places.

PLEASE DO NOT ANSWER UNLESS YOU ARE CONFIDENT YOUR ANSWER IS CORRECT.

Answer 1

Solution :

Given that,

mean = = 208 in.

standard deviation = = 1.3 in.

n = 60

=   = 208 in.

= / n = 1.3 / 60 = 0.168

P( > 208.1) = 1 - P( < 208.1)

= 1 - P[( - ) / < (208.1 - 208) / 0.168]

= 1 - P(z < 0.60)

Using z table,    

= 1 - 0.7257

= 0.2743