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

the probability is 0.0750

Explanation:

The computation of the probability is shown below;

The mean of x is

= 1.5 ÷ √79

= 0.1688

Now the probability is

= P(Z < -0.3 ÷ 0.1688) + P(\bar{x} > 0.3 ÷ 0.1688)

= P(Z < -1.78) + P(Z > 1.78)

= P(Z < -1.78) + 1 - P(Z < 1.78

= 0.0375 + 1 - 0.9625

= 0.0750

hence, the probability is 0.0750