Suppose a selective university only considers accepting students with a cumulati

Question

Suppose a selective university only considers accepting students with a cumulative grade point average of 3.2 or higher. Students below this threshold are not considered. Suppose the population of students applying to this university has a GPA that is normally distributed with a mean of 3.0 and standard deviation .4.

a)    What is the probability that a randomly selected student will meet the GPA threshold?

b)    If 50 applicants are chosen at random, what is the probability that 17 or more of them will meet the GPA threshold? (Note: You

Explanation / Answer

a) Z = 3.2 - 3.0 / .4 = 0.5

P is 0.3085 and hence 30.85% people meet the criteria

b)

p = 0.3085 , n = 50 , mean = np = 15.425 , s = sqrt(np(1-p)) = 3.266

P(X > 17 ) = P(X > (17-15.425) / 3.266) = P(Z > 0.4822) = 0.3148

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