The standardized test scores from a sample of 50 applicants to a masters program

Question

The standardized test scores from a sample of 50 applicants to a masters program indicate that none of the applicants scored below 450. A frequency distribution was formed by choosing class intervals 450 to 499, 500 to 549, and so on, with the last class having an interval from 700 to 749. Three applicants scored in the interval 450 to 499, and 14 applicants scored in the interval 500 to 549. Complete parts (a) through (d).

a. What percentage of applicants scored below 500?

b. What percentage of applicants scored between 500 and 549?

c. What percentage of applicants scored below 550?

d. What percentage of applicants scored below 750?

Explanation / Answer

We summarize all the known information in the tabular format as shown below.

Total sample size = 50

a) % population less than 500 = 3 / 50

= 6%

b) % population in 500 to 549 = 14 /50

= 28%

c) People who scored below 550 = 3 + 14 = 17 people

Thus, % of such people = 17 / 50 * 100 = 34%

d) People scoring below 750 = entire popultion as the last class where the population ends is 700-749

Thus, no. of people scoring below 750 = 50

% of such people = 50 / 50 * 100 = 100%

Hope this helps. Ask if you have any doubts.

Class Students Cumulative Below 450 0 0 450-499 3 3 500-549 14 17 550-599 600-649 650-699 700-749 50

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