The SAT is the most widely used test in the undergraduate admissions process. Scores on the...

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The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are belie

math Statistics-And-Probability

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Answer 1

Answer #1

Solution:

Given: Scores on the Math portion of the SAT are believed to be Normally distributed and range from 200 to 800.
c = confidence level = 90%
Margin of Error = E = 23
We have to find sample size n.

$n= \left ( \frac{Z_{c}\times \sigma }{E} \right )^{2}$

Population standard deviation $\sigma$ is not given, but we can estimate it using Range.

Range 0 =

L- S 0 =

800 – 200 0 =

600 0 =

0 = 150

and

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

. | 0.0 10.1 10.2 10.3 0.4 | 0.5 0.6 0.7 0.8 0.9 .01 .5040 5438 .5832 .6217 6591 6950 .02 .5080 5478 .5871 .6255 .6628 .6985

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

$n= \left ( \frac{Z_{c}\times \sigma }{E} \right )^{2}$

n = (1.645 x 150 23

n = (10.7283)

n = 115.09558

n = 116

( Sample size is always rounded up)

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