Question

On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 483 pounds and a standard deviation of 70 pounds. The cow transport truck holds 5 cows and can hold a maximum weight of 2840. If 5 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 2840

Answer 1

Answer: 0.0033

Explanation:

Let x be a random variable that denotes the weights of cows.

Given:
`\mu = 483,\ \sigma=70`

maximum weight can be hold= 2840 pounds.

Mean weight =
`(2840)/(5)` = 568 pounds

The probability their total weight will be over the maximum allowed of 2840

=
`P(X>2840)`

`P((x-\mu)/((\sigma)/(√(n)))>(568-483)/((70)/(√(5))))\\\\=P(z>2.715)\\\\=1-P(z<2.715)\\\\=1-0.9967=0.0033`

Hence, the required probability = 0.0033