Question

Suppose that the final grades in a stats course are approximately Normally distributed, with an average grade of 83 and a SD of 5. A student is randomly selected.

a.) what is the probability that the selected student received an A (at least 90)?

b.) the students know that their final grade is at the 81st percentile. Show whether or not that students grade is an A.

c.) if the students final grade is a least a B-, what is the probability that their final grade is at least an A?

Answer 1

Given that

let X be a random variable of normal distribution with mean and standard deviation

mean=mu=83

standard deviation=sigma=5

a.) probability that the selected student received an A (at least 90):

i.e

P(X <= 90) = P(X < 90.5)
                    = P(X-mu/sigma < (90.5 - 83)/5)
                    = P(z < 1.5)
                    = 0.9332

probability that the selected student received an A (at least 90) is 0.9332

b.) the students know that their final grade is at the 81st percentile.

z-value = 0.8779

score for 81th percentile is
x = 83 + 0.8779*5 = 87.3895

criterias for different grades are not given.