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

Answer:

$N= 4543$ Labrador retrievers

Step-by-step 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:

$P(X$

We calculate the Z-score for X =65

$Z = \frac{X-\mu}{\sigma}\\\\Z =\frac{65-62.5}{65}=1$

So

$P(X$

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

$P(Z$.

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

$N = P(X$

$N = 0.8413*5400$

$N= 4543$ Labrador retrievers