5,687.3 mi to the nearest mile
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The standard form of a quadratic equation is
,
where ,
, and
are coefficients. You want to get the given equation into this form. You can accomplish this by putting all the non-zero values on the left side on the equation.
In this case, the given equation is
Since is on the right side of the equation, we subtract that from both sides. The resulting equation is
Looking at the standard form equation , we can see that
Using the normal distribution, it is found that there are 68 students with scores between 72 and 82.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
The proportion of students with scores between 72 and 82 is the <u>p-value of Z when X = 82 subtracted by the p-value of Z when X = 72</u>.
X = 82:
Z = 1
Z = 1 has a p-value of 0.84.
X = 72:
Z = 0
Z = 0 has a p-value of 0.5.
0.84 - 0.5 = 0.34.
Out of 200 students, the number is given by:
0.34 x 200 = 68 students with scores between 72 and 82.
More can be learned about the normal distribution at brainly.com/question/24663213
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