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

Step-by-step 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 , $z=\dfrac{x-\mu}{\sigma}$ the z-score corresponding to x= 65 will be :-

$z=\dfrac{65-62.5}{2.5}=1$

Using the z-value table , we have

$P(z$

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

Now, the number of people weigh less than 65 lb = $0.8413\times5400$

$=4543.02\approx4543$

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