Question

PROBLEM 3

The average grade point average (GPA) of undergraduate students in New York is normally distributed with a population mean of 2.8 and a population standard deviation of 0.75

(I) The percentage of students with GPA's between 2 and 2.5 is

CHOICE =

(II) The percentage of students with GPA's above 3.0 is:

PERCENTAGE =

(III) Above what GPA will the top 5% of the students be (i.e., compute the 95th percentile):

GPA =

(IV) If a sample of 25 students is taken, what is the probability that the sample mean GPA will be between 2.8 and 2.75?

CHOICE =

Answer 1

This is a normal distribution question with

a) x₁ = 2
x₂ = 2.5
P(2.0 < x < 2.5)=?

This implies that
P(2.0 < x < 2.5) = P(-1.0667 < z < -0.4) = 0.2015
b) x = 3
P(x > 3.0)=?

z = 0.2667
This implies that
P(x > 3.0) = P(z > 0.2667) = 0.3949
c) Given in the question
P(X < x) = 0.95
This implies that
P(Z < 1.645) = 0.95
With the help of formula for z, we can say that

x = 4.0337
Sample size (n) = 25
Since we know that

d) x₁ = 2.75
x₂ = 2.8
P(2.75 < x < 2.8)=?

This implies that
P(2.75 < x < 2.8) = P(-0.3333<z<0) = 0.1304
PS: you have to refer z score table to find the final probabilities.
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