Question

1. According to the U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school.

According to the central limit theorem, what are the mean and standard error of the distribution of sample means for a sample of 50 students?

a. 50 and 21.1

b. 21.1 and 4.8

c. 21.1 and 0.68

d. 21.1 and 0.10  

2. According to the U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school.

What is the z-score for a mean of 19.6 from a sample of 50 students from this population? Round your answer to two decimal places.

3. 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 22 on this test?

4. 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.

Answer 1

Q.1) According to the central limit theorem, the mean and standard error of the distribution of sample means are,

Given that,

Mean = 21.1 and standard deviation = 4.8

sample size ( n ) = 50

Therefore, mean and standard error of the distributionof sample means are,

Amswer: c) 21.1 and 0.68

Q.2) we want to find, z-score for sample mean = 19.6

Z-score = -2.2121

Q.3) Given that,

Mean = 35.3 and standard deviation = 8.6

We want to find, z-score for X = 22

z-score = -1.55

Q.4) We want to find, P(X < 22)

P(X < 22) = P(Z < -1.55) = 0.0606

Therefore, proportion of the population falls below a score of 22 on this test is 0.0606