Question

Human body temperatures are normally distributed with a mean of 37.0 degrees and a standard deviation of 0.35 degrees. If a sample of 148 people is selected, determine the expected number of people in the sample with body temperatures above 37.5 degrees

Answer 1

11 people

Explanation:

Mean body temperature = u = 37.0 degrees

Standard Deviation =
`\sigma` = 0.35 degrees

Sample Size = n = 148

We have to find how many people in a sample of 148 will have body temperatures above 37.5 degrees. For this first we need to find what is the percentage of people with body temperatures above 37.5 degrees. This can be done by converting 37.5 to equivalent z score and using z table to find what percentage would be above that value.

The formula for z score:

`z=(x-u)/(\sigma)`

Using the values, we get:

`z=(37.5-37)/(0.35)=1.43`

So now from z table we have to find what is the percentage of the z score being above 1.43, which comes out to be 0.0764 or 7.64%

This means, 7.64% of people will have body temperatures above 37.5 degrees. This means from a sample of 148, number of people with body temperatures above 37.5 degrees would be:

7.64 % of 148 = 0.0764 x 148 = 11 (rounded to nearest integer)

11 people are expected to have the body temperatures above 37.5 degrees

Answer 2

12

Explanation:

The expected value is
`n*p`, where n=148 is the sample size and
`p=P(x\:>\:37.5)`.

We calculate the z-score of 37.5 using the formula:

`z=(x-\mu)/(\sigma)`

`z=(37.5-37.0)/(0.35)`

`z=(0.5)/(0.35)=1.43`

From the standard normal distribution table, the area to the left of 1.43 is 0.9236.

`\implies P(x\:>\:37.5)=1-0.9236=0.0764`.

The expected number of people in the sample with body temperatures above 37.5 degrees is
`0.0764*148=11.3072=12`

We don't have a fractional human being, so the rule of thumb is to round up.