Question

Human body temperatures have a mean of 98.20degrees°F and a standard deviation of 0.62degrees°F. ​Sally's temperature can be described by zequals=minus−1.5. What is her​ temperature? Round your answer to the nearest hundredth.

Answer 1

Her temperature is 97.27ºF.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

`\mu = 98.2, \sigma = 0.62`

Z = -1.5. What is her​ temperature?

Her temperature is X when Z = -1.5. So

`Z = (X - \mu)/(\sigma)`

`-1.5 = (X - 98.2)/(0.62)`

`X - 98.2 = -1.5*0.62`

`X = 97.27`

Her temperature is 97.27ºF.