Question

a.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

Using the z-score found for the question above, what proportion of the population falls below a score of 22 on this test? Round your answer to four decimal places.

b.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

What is the z-score for a student who gets a 43 on this test?

c.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

Using the z-score found for the question above, what proportion of the population falls below a score of 43 on this test?

d.) What proportion of the normal distribution is below a z-score of -1.69. Round your answer to four decimal places.

Answer 1

Part a)

Given :-   = 35.3 = 8.6

what proportion of the population falls below a score of 22 on this test

X N ( 35.3 , 8.6)

Calculating Z score  

Z = -1.55

P ( X < 22 ) = P ( < )

P ( X < 22 ) = P ( Z < -1.55)

P ( X < 22 ) = 0.0606

To find the percentage 0.0606*100 = 6.06%

6.06% of populaiton is fall below the score of 22 on the test

Part b)  

= 35.3 = 8.6

What is the z-score for a student who gets a 43 on this test?

X N ( 35.3 , 8.6)

Calculating Z score  

Z = 0.8953

Part c)

Given :-   = 35.3 = 8.6

what proportion of the population falls below a score of 43 on this test

X N ( 35.3 , 8.6)

Calculating Z score  

Z = 0.8953

P ( X < 43 ) = P ( < )

P ( X < 43 ) = P ( Z < 0.8953 )

P ( X < 43 ) = 0.8159

To find the percentage 0.8159*100 = 81.59%

81.59% of populaiton is fall below the score of 43 on the test

Part d)  What proportion of the normal distribution is below a z-score of -1.69.

P ( Z < -1.69) = 0.0455

To find the percentage 0.0455*100 = 4.55%

4.55% of population is below the Z score of -1.69