Question

At one college, the distribution of GPA's is bell-shaped with a mean of 2.8 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.0 and 3.6?

A. 95.44%

B. 68.26%

C. 84.13%

D. 99.74%

Answer 1

Given,

= 2.8 , = 0.4

We convert this to standard normal as

P( X < x ) = P( Z < x - / )

So,

P( 2 < X < 3.6) = P( X < 3.6) - P( X< 2 )

= P( Z< 3.6 - 2.8 / 0.4) - P( Z < 2 - 2.8 / 0.4)

= P( Z < 2) - P (Z < -2)

= P( Z < 2) - ( 1 - P( Z < 2) )

= 0.9772 - ( 1 - 0.9772)

= 0.9544

= 95.44%