Question

The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of 4 pounds.

Answer 1

Answer:

A) 8

Step-by-step explanation:

Mean weight = u = 25 pounds

Standard Deviation = $\sigma$ = 4 pounds

We have to find how many beagles out of 75 will weigh more than 30. Since the data is normally distributed, we can use z score to find this value. First we will what is the percentage(probability) of a randomly selected beagle to weigh more than x = 30 pounds, using this percentage we can then find our answer.

The formula for z score is:

$z=\frac{x-u}{\sigma}$

Using the values, we get:

$z=\frac{30-25}{4}=1.25$

So, P(Weight > 30) is equivalent to P(z > 1.25). Using the z table, we can write:

P(z > 1.25) = P(Weight > 30) = 0.1056

This, 0.1056 or 10.56% of the beagles are expected to weigh more than 30 pounds.

So,out of 75 beagles, 10.56% of 75 are expected to weigh more than 30 pounds.

10.56% of 75 = 0.1056 x 75 = 7.92 = 8 (rounding to nearest integer)

Therefore, out of 75 beagles 8 are expected to weigh more than 30 pounds.