Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2.8 and a mean diameter of 210 inches. If 84 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be greater than 209.7 inches? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 210

standard deviation = = 2.8

n = 84

= 210 and

= / n = 2.8 / 84 = 0.3055

P(? > 209.7) = 1 - P( < 209.7) = 1 - P(( - ) / < (209.7 - 210) / 0.3055) = 1 - P(z < -0.9820)

    Using standard normal table,

P( > 210) = 1 - 0.1631 = 0.8369

Probability = 0.8369