Question

Suppose that the weights of 5400 registered female Labrador retrievers in the United States are distributed normally with a mean of 62.5 lb and a standard deviation of 2.5 lb.

Approximately how many of the Labrador retrievers weigh less than 65 lb?

Enter your answer in the box.

Answer 1

`N= 4543` Labrador retrievers

Explanation:

We know that the mean
`\mu` is:

`\mu = 62.5`

and the standard deviation
`\sigma` is:

`\sigma=2.5`

The probability that a randomly selected Labrador retriever weighs less than 65 pounds is:

`P(X<65)`

We calculate the Z-score for X =65

`Z = (X-\mu)/(\sigma)\\\\Z =(65-62.5)/(65)=1`

So

`P(X<65) = P(Z<1)`

Looking in the table for the standard normal distribution we have to:

`P(Z<1) =0.8413`.

Finally the amount N of Labrador retrievers that weigh less than 65 pounds is:

`N = P(X<65) *5400`

`N = 0.8413*5400`

`N= 4543` Labrador retrievers