If a set of grades on statistics examination are approximately normally distributed with a mean of 74 and a standard deviation of 7.9, what is the lowest B if the top 10% of the students are given A's and the next 25% are given B's?

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Answer 1 · 2018-04-05T07:03:09

The lowest B grade is #77#

Given: normally distributed data, #mu = 74, sigma = 7.9#; A = top 10%, B is up to 25% less,

The probability for A's #= 1 - .10 = .90; " or "90%#

The probability for a B:
Lower percent value: #.1 + .25 = .35; " "1-.35 = .65#

is between #65% " and " 90 %#

#z = (x - mu)/sigma#

From a z-table the #.65# percent is about half way between #z = 0.38 " and " z = 0.39#. So let #z = 0.385#

Solve for the #x# value to find the lowest B grade:

#0.385 = (x - 74)/7.9#

#x = 0.385 * 7.9 + 74 = 77#

The lowest B grade is #77#