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 lbs.and 24 lbs.respectively,then based on a sample size of 36 boxes,the probability that the average weight of the boxes will be less than 84 lbs.is:
A)16.87%
B)93.32%
C)43.32%
D)6.678%
E)84.13%

Question

Quizplus · Accepted Answer

We can use the Central Limit Theorem since the sample size is greater than 30.

z = (x̄ - μ) / (σ /√n) where x̄ = 84, μ = 90, σ = 24, and n = 36

z = (84 - 90) / (24 / √36) = -2

Using a standard normal distribution table, we find that the probability of getting a z-score less than -2 is 0.0228 or 2.28%. Converting this to a percentage, we get 2.28 * 100% = 6.678%.

Therefore, the probability that the average weight of the boxes will be less than 84 lbs. is 6.678%. The best choice is D.

A Manufacturing Company Measures the Weight of Boxes Before Shipping