Louisj1j2
Answered

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?

Verified Answer :

meerkat18

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

JeanaShupp

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

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

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

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

\(=4543.02\approx4543\)

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

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