# On the final examination in Engineering Data Analysis, the mean was 72

On the final examination in Engineering Data Analysis, the mean was 72 and the standard deviation was 15.
a. Determine the standard scores (z-values) of students receiving the grade of 65.
b. Determine the standard scores (z-values) of students receiving the grade of 85
c. Determine the probability that a student will score greater than 75.
d. Determine the probability that a student will score lower than 65.
e. Find the grade corresponding to a standard score of 1.

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Laura Worden
Given,
$$\displaystyle\mu={72}$$
$$\displaystyle\sigma={15}$$
a)
The standard scores (z-values) of students receiving the grade of 65 is,
$$\displaystyle{z}={\frac{{{x}-\mu}}{{\sigma}}}$$
$$\displaystyle={\frac{{{65}-{72}}}{{{15}}}}$$
=-0.47
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Jeremy Merritt
b)
The standard scores (z-values) of students receiving the grade of 85 is,
$$\displaystyle{z}={\frac{{{x}-\mu}}{{\sigma}}}$$
$$\displaystyle={\frac{{{85}-{72}}}{{{15}}}}$$
=0.87