During the 52 week period ranging from 01/01/2002 to 12/30/2002, a bottle manufacturing company tracked the number of cases (of bottles) it lost in transit on a weekly basis. The average number of cases lost per week was 30.8 with a standard deviation of 2.6. The number of weeks in which it lost more than 36 cases, absent any additional information or assumption, is

approximately 2 weeks

Explanation:

Assuming normal distribution, we have

mean m = 30.8

standard deviation s = 2.6

The standard random variable is given by Z = (x - 30.8) / 2.6

where x denotes the number of cases lost

we are to evaluate probability of losing more than 36 i. e P (x > 36)

This will be P (Z > (36 - 30.8) / 2.6) = P (Z > 2)

using the z-score table, we have this probability to be 0.0228

so the number of weeks is given by 52*0.228 = 1.19

which is approximately 2