Question

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

Answer 1

`Z=\frac{X-\mu}\sigma\iff-1.5=(X-98.20^\circ)/(0.62^\circ)\implies X\approx97.27^\circ`

Answer 2

`97.27^(o)F`

Explanation:

We have been given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°. Sally's temperature can be described by z = -1.5.

To find Sally's temperature we will use z-score formula.

`z=(x-\mu)/(\sigma)`, where
`\mu` = Mean,
`\sigma`= Standard deviation.

Let us substitute our given values in z-score formula.

`-1.5=(x-98.20)/(0.62)`

Multiply 0.62 to both sides of equation.

`0.62*-1.5=0.62* (x-98.20)/(0.62)`

`-0.93=x-98.20`

Add 98.20 to both sides of equation.

`-0.93+98.20=x-98.20+98.20`

`97.27=x`

Therefore, Sally's temperature will be 97.27 degrees Fahrenheit.