Question

Students Born in USA

MEAN GPA: 3.05 STD DEVIATION: .511

MEAN AGE: 27 STD DEVIATION: 10

MEAN HOURS SPEND ON HW: 8.50 STD DEVIATION: 4.72

STUDENTS BORN OUTSIDE USA

MEAN GPA: 3.26 STD DEVIATION: .428

MEAN AGE: 31 STD DEVIATIONS: 10.5

MEAN HOURS SPENT ON HW: 14.13 STD DEVIATION: 10.4

1. If one student is randomly selected from the USA born group, find the probability of getting someone with a GPA greater than 3.88.

2. If one student is randomly selected from the Non-USA born group, find the probability of getting someone with a GPA greater than 3.88.

3. If one student is randomly selected from the USA born group, find the probability of getting someone between the ages of 20 and 25. 4. If 9 students are randomly selected from the Non-USA born group, find the probability that their mean age is between 22 and 37. 5. If 25 students are randomly selected from the USA born group, find the probability that their mean GPA is between 2.50 and 3.50.

Answer 1

Students Born in USA

MEAN GPA: 3.05 STD DEVIATION: .511

MEAN AGE: 27 STD DEVIATION: 10

MEAN HOURS SPEND ON HW: 8.50 STD DEVIATION: 4.72

STUDENTS BORN OUTSIDE USA

MEAN GPA: 3.26 STD DEVIATION: .428

MEAN AGE: 31 STD DEVIATIONS: 10.5

MEAN HOURS SPENT ON HW: 14.13 STD DEVIATION: 10.4

1. If one student is randomly selected from the USA born group, find the probability of getting someone with a GPA greater than 3.88.

          z = (x-µ)/σ

z value for 3.88, z =(3.88-3.05)/0.511 = 1.62

P( x >3.88) = P( z > 1.62) =0.0526

2. If one student is randomly selected from the Non-USA born group, find the probability of getting someone with a GPA greater than 3.88.

z value for 3.88, z =(3.88-3.26)/0.428 = 1.45

P( x >3.88) = P( z > 1.45) =0.0735

3. If one student is randomly selected from the USA born group, find the probability of getting someone between the ages of 20 and 25.

z value for 20, z =(20-27)/10 = -0.7

z value for 25 z =(20-25)/10 = -0.5

P( 20<x<25) = P( -0.7 <z< -0.5)= P( z < -0.5)-P( z < -0.7)

= 0.3085-0.242=0.0665

4. If 9 students are randomly selected from the Non-USA born group, find the probability that their mean age is between 22 and 37.

Standard error = sd/sqrt(n) = 10.5/sqrt(9) =3.5

z value for 22, z = (22-31)/3.5 = -2.57

z value for 37, z = (37-31)/3.5 = 1.71

P( 22 < mean x<37) = P( -2.57<z<1.71) = P( z < 1.71)-P( z< -2.57)

=0.9564-0.0051

=0.9513

5. If 25 students are randomly selected from the USA born group, find the probability that their mean GPA is between 2.50 and 3.50.

Standard error = sd/sqrt(n) = 0.511/sqrt(25) =0.1022

z value for 2.50, z =(2.50-3.05)/0.1022 =-5.38

z value for 3.50, z =(3.50-3.05)/0.1022 = 4.40

P( 2.50< mean x < 3.50) = P( -5.38<z<4.40)

P( z <4.40) –P( z <-5.38)=1.0-0.0

=1