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?

Answer 1

Answer: 4543

Explanation:

Given : The weights of 5400 registered female Labrador retrievers in the United States are distributed normally with a
`\mu=62.5\ lb` and a standard deviation of
`\sigma=2.5\ lb`.

Using formula ,
`z=(x-\mu)/(\sigma)` the z-score corresponding to x= 65 will be :-

`z=(65-62.5)/(2.5)=1`

Using the z-value table , we have

`P(z<1)=0.8413447\approx0.8413`

i.e. Proportion of people weigh less than 65 lb= 0.8413

Now, the number of people weigh less than 65 lb =
`0.8413*5400`

`=4543.02\approx4543`

Hence, the approximate number of people weigh less than 65 lb= 4543

Answer 2

we are given in the problem the data on the number of respondents, the mean and the standard deviation. In this problem, we find first the z-score through z = (65-62.5)/2.5 = 1. We find next the probability of this z-score then multiply the probability to the number of respondents. That is the answer