Question

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3.2.21. A professor in a large statistics class has a grading policy such that only the 15% of the students with the highest scores will receive the grade A. The mean score for this class is 72 with a standard deviation of 6. Assuming that all the grades for this class follow a normal probability distribution, what is the minimum score that a student in this class has to get to receive an A grade?

Answer 1

Solution:-

Given that,

mean = $\mu$ = 72

standard deviation = $\sigma$ = 6

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15  

= P(Z < z) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.036) = 0.85  

z = 1.036

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.036 * 6 + 72

x = 78.22

minimum score = 78.22