Question

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lb and 24 lb, respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will exceed 94 lb? 34.13% 84.13% 15.87% 56.36% 16.87%

Answer 1

We want to find the probability that the average weight of the boxes will exceed 94 lb.

Sample mean is approximately normal distributed with mean μ = 90 lb and SD is 24 /

We use central limit theorem because sample size is greater than 30.

Here, we solve this problem by standardization.

P(  > 94) = P { ( – μ) / (σ / ) > (94 - 90) / (24 /)}

                                           = P (z > 1)

                                             = 1 - P(Z ≤ 1)          

                                             =1 – 0.8413 …..……..using statistical table

P(   > 94) = 1 – 0.8413 = 0.1587

The probability that the average weight of the boxes will exceed 94 lb is 15.87%