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at one college, gpa's are normally distributed with a mean of 2.8 and a standard deviation of 0.4. about what percentage of students at the college have a gpa below 2.4?

Sagot :

The percentage of students at the college have a gpa below 2.4 is 15.87%.

Given,

The gpa's are normally distributed with given mean and SD.

mean [tex]\bar{x}[/tex]= 2.8

SD σ=0.4

raw score=2.4

The z score can be calculated by using the formula

z=[tex]\frac{x-\bar{x}}{\sigma}[/tex]

z=[tex]\frac{2.4-2.8}{0.4}[/tex]

[tex]z=\frac{-0.4}{0.4}[/tex]

z=-1

Using the z table we get the value P(z<-1), it is 0.8413, as it is less than we subtract it from 1 and we get 0.1587. As the value we got is negative, we used left tail z table to get the value of the z.

To get the percentage, we have to multiply by 100,

0.1587 x100

=15.87%

Therefore, the percentage of students at the college with gpa below 2.4 is 15.87%.

To know more about z table refer here:

https://brainly.com/question/29138590#

#SPJ4

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