Answer:
The (population) <em>standard deviation</em> is 26 miles or miles.
Step-by-step explanation:
We can solve this question using the concept of <em>z-score</em> or <em>standardized value, </em>which is given by the formula:
[1]
Where
is the <em>z-score</em>.
is the <em>raw score</em>.
is the <em>population's mean</em>.
is the <em>population standard deviation</em>.
Analyzing the question, we have the following data to solve this question:
- The random variable <em>number of miles driven by day </em>is <em>normally distributed</em>.
- The population's mean is miles.
- The raw score, that is, the value we want to standardize, is miles.
- The <em>z-score</em> is . It tells us that the raw value (or raw score) is <em>below</em> the population mean because it is <em>negative</em>. It also tells us that this value is 0.7 <em>standard deviations units</em> (below) from .
Therefore, using all this information, we can determine the (population) <em>standard deviation</em> using formula [1].
Then, substituting each value in this formula:
Solving it for
Multiplying each side of the formula by
Multiplying each side of the formula by
Then, this formula, solved for , will permit us to find the value for the <em>population standard deviation </em>asked in the question.
Thus, the (population) <em>standard deviation</em> is 26 miles or miles.