Question

Corker Industries produces composite corks for wine that have a diameter that is uniformly distributed between 0.9 and 1.1 cm. A new customer wanting to purchase Corker’s corks currently has specifications that require corks whose specifications are from 0.85 to 1.0 cm. (a) What percentage of Corker’s corks will meet the customer’s current specifications? (b) What should be the mean of the customer’s specifications in order to have the greatest proportion of Corker’s corks meet specifications?

Answer 1

X ~ U(0.9 , 1.1)

a) P(0.85 < X < 1.0) = P(0.85 < X < 0.9) + P(0.9 < X < 1.0)

                                = 0 + (1 - 0.9) / (1.1 - 0.9)

                                = 0.5

b) The mean should be (0.85 + 1.0) / 2 = 0.925