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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.

Respuesta :

[tex]Z=\dfrac{X-\mu}\sigma\iff-1.5=\dfrac{X-98.20^\circ}{0.62^\circ}\implies X\approx97.27^\circ[/tex]

Answer:

[tex]97.27^{o}F[/tex]

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.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where [tex]\mu[/tex] = Mean, [tex]\sigma[/tex]= Standard deviation.

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

[tex]-1.5=\frac{x-98.20}{0.62}[/tex]

Multiply 0.62 to both sides of equation.

[tex]0.62\times-1.5=0.62\times \frac{x-98.20}{0.62}[/tex]

[tex]-0.93=x-98.20[/tex]

Add 98.20 to both sides of equation.

[tex]-0.93+98.20=x-98.20+98.20[/tex]

[tex]97.27=x[/tex]

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