 On the final examination in Engineering Data Analysis, the mean was 72 kuvitia9f 2021-12-08 Answered
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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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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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