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.
\(Z=\dfrac{X-\mu}\sigma\iff-1.5=\dfrac{X-98.20^\circ}{0.62^\circ}\implies X\approx97.27^\circ\)
Answer:
\(97.27^{o}F\)
Step-by-step 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.
\(z=\frac{x-\mu}{\sigma}\), where \(\mu\) = Mean, \(\sigma\)= Standard deviation.
Let us substitute our given values in z-score formula.
\(-1.5=\frac{x-98.20}{0.62}\)
Multiply 0.62 to both sides of equation.
\(0.62\times-1.5=0.62\times \frac{x-98.20}{0.62}\)
\(-0.93=x-98.20\)
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.