The marks on a Statistics test are normally distributed with

The marks on a Statistics test are normally distributed with a mean of 62 and a variance of 225. If the instructor wishes to assign B\'s or higher to the top 30% of the students in the class, what mark is required to get a B or higher?

The answer is 69.87, but I can\'t figure out why every solution lists z = .5244. I just need help on the z part.

Solution

let k be the marks required to get a B

P( X > k ) = 0.3

P(X<k) = 1-0.3 = 0.7

P( Z < k-mean/std) = 0.7

=>

k-mean/std = invnorm(0.7) = 0.5244 ( from normal distribution table) (area under z<0.5244 is 0.7)

k - 62/15 = 0.5244

=>

k = 69.87 ..............ans