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Lostsunrise [7]
3 years ago
14

According to the U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics 1,026,0

00 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
Mathematics
1 answer:
Andreyy893 years ago
7 0

Answer:

The correct option is C) 21.1 and 0.68  

Step-by-step explanation:

Consider the provided information.

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.

Therefore μ = 21.1 and σ = 4.8

It is given that the sample of 50 students;

Thus, sample size ( n ) = 50

According to the central limit theorem,

\mu_{\bar x}=\mu\ and \ \sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}

Therefore

\mu_{\bar x}=21.1

\sigma_{\bar x}=\frac{4.8}{\sqrt{50}}

\sigma_{\bar x}=0.68

Hence, the correct option is C) 21.1 and 0.68

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Step-by-step explanation:

Given equation is:

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In order to find that which values of x makes the equation true, we have to put each value of x in the equation. When both sides of equations will be equal, that value of x will be true for the equation.

Putting x = 2

3(2 + 2) + 2 = 2(2) + 16\\3(4)+2 = 4+16\\12+2 = 20\\14 \neq 20

Putting x = 3

3(3 + 2) + 3 = 2(3) + 16\\3(5)+3 = 6+16\\17+3 = 22\\20 \neq 22

Putting x=4

3(4+2)+4 = 2(4)+16\\3(6)+4 = 8+16\\18+4 = 24\\22 \neq 24

Putting x = 5

3(5+2)+5 = 2(5)+16\\3(7)+5 = 10+16\\21+5 = 26\\26 = 26

The equation is true for x = 5

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The correct answer is: Option D) 5

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