Question

The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. if the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?

Answer 1

In this case, the z-score for 36 months would be (-4/8) or -0.50. Taking the standard distribution into account, a z-score of +0.50 gives a value of .3085. Taking (1-.3085) gives the amount of the tail to the right of a negative z-score, which would be .6915. Therefore, 69.15% of 1,000,000 pairs, or 691,500 pairs, will need replacement before the end of 36 months.