Question

The mean quantitative score on a standardized test for female college-bound high school seniors was

550

The scores are approximately Normally distributed with a population standard deviation of

50

A scholarship committee wants to give awards to college-bound women who score at the

96TH

percentile or above on the test. What score does an applicant need? Complete parts (a) through (g) below.The mean quantitative score on a standardized test for female college-bound high school seniors was

550

The scores are approximately Normally distributed with a population standard deviation of

50

A scholarship committee wants to give awards to college-bound women who score at the

96

percentile or above on the test. What score does an applicant need? Complete parts (a) through (g) below.

A.

The 96th percentile has 96% of the area to the left because it is higher than 96% of the scores. The table above gives the areas to the left of z-scores. Therefore, we look for 0.9600 in the interior part of the table. Use the Normal table given above to locate the area closest to 0.9600. Then report the z-score for that area.

Answer #1

Solution:-

Given that,

mean = = 550

standard deviation = = 50

Using standard normal table,

P(Z > z) = 96%

= 1 - P(Z < z) = 0.96

= P(Z < z) = 1 - 0.96

= P(Z < z ) = 0.04

= P(Z < -1.75 ) = 0.04

z = -1.75

Using z-score formula,

x = z * +

x = -1.75 * 50 + 550

x = 462.5

test score = 463

One year, many college-bound high school seniors in the U.S.
took the Scholastic Aptitude Test (SAT). For the verbal portion of
this test, the mean was 425 and the standard deviation was 110.
Based on this information:
a) What proportion scored 500 or above? Draw the picture!
b) What proportion of the students would be expected to score
between 350 and 550? Draw the picture.

One year, many college-bound high school seniors in the U.S.
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this test, the mean was 425 and the standard deviation was 110.
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a) What proportion scored 500 or above? Draw the picture!
b) What proportion of the students would be expected to score
between 350 and 550? Draw the picture.
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