I got a, and b right, but having a hard time with c. A set of final examination

Question

I got a, and b right, but having a hard time with c.

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 77 and a standard deviation of 8. Complete parts (a) through (d. a. What is the probability that a student scored below 91 on this exam? The probability that a student scored below 91 is 0.9599 (Round to four decimal places as needed.) b. What is the probability that a student scored between 69 and 99? The probability that a student scored between 69 and 99 is 0.8383 Round to four decimal places as needed.) C. The probability is 5% that a student taking the test scores higher than what grade? The probability is 5% that a student taking the test scores higher than D (Round to the nearest integer as needed.)

Explanation / Answer

z score corresponding to 5% area to its right i.e. 95th percentile = 1.645

Hence,

Probability is 5% that test score is higher than (77 + 1.645*8) i.e. 90

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