Mathematics, 11.03.2020 18:33 mszeew

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

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Answer from: Laydax1587

Sally's temperature is 97.27 °F.

Step-by-step explanation:

All the information given in the question tells us that the human body temperatures are normally distributed with a population's mean = 98.20°F and a standard deviation = 0.62°F.

The question gives us Sally's temperature in a z-score. We have to remember that the standard normal distribution is a particular case of a normal distribution where the mean = 0 and the standard deviation = 1.

Using the standard normal distribution, we can determine every probability associated with a normal distribution "transforming" the raw scores, coming from normally distributed data, into z-scores.

A z-score gives us the distance from the population's mean and is in standard deviation units. So, a z = 1.5 tells us that the value is 1.5 standard deviations above the mean. Conversely, a z = -1.5 tells us that the raw score is also 1.5 standard deviation from the mean, but in the opposite direction, that is, below the mean.

The formula for a z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ (1)

Where

$\\ x\;is\;the\;raw\;score$ .

$\\ \mu\;is\;the\;population\;mean$ .

$\\ \sigma\;is\;the\;population\;standard\;deviation$ .

Then to find x (or the raw score, that is, Sally's temperature), we need to solve the formula (1) for it to finally solve the question.

Then

$\\ \mu = 98.20^\circF$ °F

$\\ \sigma = 0.62^\circF$ °F

$\\ z = -1.5$

Thus (with no units)

$\\ -1.5 = \frac{x - 98.20}{0.62}$

$\\ (-1.5*0.62) = x - 98.20$

$\\ (-1.5*0.62) + 98.20 = x$

$\\ x = (-1.5*0.62) + 98.20$

$\\ -0.93 + 98.20$

$\\ x = 97.27$ °F

Thus, Sally's temperature is $\\ x = 97.27$ °F (rounding the answer to the nearest hundredth).

Answer from: hurtadocrv

Sally's temperature is 97.27° F .

Step-by-step explanation:

We are given that Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F.

Let X = Human body temperatures

So, X ~ N( $\mu = 98.20,\sigma^{2}=0.62^{2}$ )

The z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Let Sally's temperature be x ; we are given that Sally's temperature can be described by z = -1.5; i.e.;

-1.5 = $\frac{x-98.20}{0.62}$

x = 98.20 - (1.5 * 0.62)

x = 98.20 - 0.93 = 97.27° F

Therefore, Sally's temperature is 97.27° F .

Answer from: Quest

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

Answer from: Quest

The full question isn’t shown. part of it is cut off
Ihave a test on this i need an in depth explanation i tried to solve this multiple ways