SOLUTION: On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 506 pounds and a standard deviation of 84 pounds. The cow transport truck holds 10 c

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Question 1147746: On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 506 pounds and a standard deviation of 84 pounds. The cow transport truck holds 10 cows and can hold a maximum weight of 5430. If 10 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 5430? (This is the same as asking what is the probability that their mean weight is over 543.)
(Give answer correct to at least three decimal places.)
probability =
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
First, you want to find the standard deviation of the sample. You do this by taking the standard deviation of the population and dividing it by the square root of the number of items in the sample:

84%2Fsqrt%2810%29 = 84%2F3.1623 = 26.5629

Zscore = %28x+-+mean%29%2FSD+sample

Zscore = %28543+-+506%29%2F26.5629 = 37%2F26.5629 = 1.39

Go to a z-table and look up +1.39. At a z-score of +1.39, the area to the left of the curve is 0.9177. However, we want to find the probability that the mean weight is GREATER than 543 lbs., so we want to find the area to the RIGHT of the curve. To do this, we subtract 0.9177 from 1. This comes out to 0.0823.

So, there is a 0.0823 probability the mean weight is over 543 lbs. (Or, to answer the original question, there is a 0.0823 probability the cows' combined weight will exceed 5430 lbs.)