What is the value of this expression if h = 8,3 = -1, and k = –12?
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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:
(1)
Where
.
.
.
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
°F
°F
Thus (with no units)
°F
Thus, Sally's temperature is °F (rounding the answer to the nearest hundredth).