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Anna007 [38]
3 years ago
15

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.
Mathematics
2 answers:
irina1246 [14]3 years ago
8 0

Answer:

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 <em>z-score</em>. We have to remember that the <em>standard normal distribution</em> is a particular case of a <em>normal distribution</em> where the mean = 0 and the standard deviation = 1.

Using <em>the standard normal distribution,</em> 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 <em>above the mean</em>. 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, <em>below the mean</em>.

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 <em>x </em>(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).

svp [43]3 years ago
4 0

Answer:

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 .

 

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