Question

A certain manufacturing procedure produces items that have a mean weight of 55 pounds and a standard deviation of 3.2 pounds. With what minimum probability can we assert that the weight of a randomly selected item produced by this procedure is between 45.4 pounds and 64.6 pounds?

Answer 1

Solution :

Given that,

mean = = 55

standard deviation = = 3.2

P(45.4 < x < 64.6) = P((45.4 - 55 / 3.2) < (x - ) / < (64.6 - 55 ) / 3.2) )

P(45.4 < x < 64.6) = P(-3 < z < 3)

P(45.4 < x < 64.6) = P(z < 3) - P(z < -3)

P(45.4 < x < 64.6) = 0.9987 - 0.0013

Probability = 0.9974

Minimum probabilioty = 0.9974