Assume that human body temperatures are normally distributed with a mean of 98.20 degrees F and a standard deviation of 0.61 degrees F.

Question

Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature​ be, if we want only​ 5.0% of healthy people to exceed​ it?

Answer 1

I assume that this question is asking for you to look at a standard normal distribution, and decide what the bottom five percent of the distribution is that corresponds to the values provided.

If we look at the standard normal distribution, notice that the bottom five percent of the distribution is associated with a z-score of -1.64.

Now we have all the information necessary to answer the question:

Mu = 98.20

Sigma = 0.61,

z = -1.64.

The next piece requires a bit of simple algebra. Notice that the equation for a z-score is:

z = ( x - Mu ) / Sigma,

where x refers to a score, Mu refers to the population mean, and Sigma refers to the population standard deviation. In this case, we want to solve for "x".

To solve for x, we need to use algebra to get x to one side of the equation:

z = ( x - Mu ) / Sigma,

[multiply both sides of equation by Sigma, then Sigma drops out on right-hand side]

z * Sigma = x - Mu,

[Now add Mu to both sides of the equation, and you can solve for x]

x = Mu + z * Sigma.

Now let's plug in your values:

x = 98.20 - 1.64 * 0.61 = 97.20 degrees.