Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.54 and a standard deviation of 0.42. Using the empirical rule, what percentage of the students have grade point averages that are at least 3.8? Please do not round your answer.

Answer 1

Solution:

Given that,

= 2.54

= 0.5

So,

Using empirical rule

P ( x 3.8 )

P( - 3< X < + 3) = 99.7%

P(2.54 - 3-*0.5< X < 2.54 + 3*0.5 ) = 99.7%

P(2.54 - 1.5< X < 2.54 + 1.5 ) = 99.7%

P(1.04 < X < 4.04 ) = 99.7%

P ( x ≤ 1.04 ) =0.0015

P ( x ≤1.54 ) =0.025

P ( x ≤ 2.04) =0.16

P ( x ≤ 3.04 ) =0.84

P ( x ≤ 3.54) =0.975

P ( x ≤ 4.04 ) =0.9985