Question

Listed below are the ACT scores of 40 randomly selected students at a major university. (Use technology if you wish, Excel) 18 16 26 19 22 25 26 19 13 14 25 14 15 19 25 24 24 21 19 20 24 23 17 21 20 25 18 23 19 18 15 22 1912 18 13 13 21 19 17 W = 26-12= 1.75=2 (a) Construct a frequency table for the data, using 8 classes. Show W. Using the table, answer the following questions: (b) If the university wants to accept the top 90% of the applicants, what should the minimum score be? (c) If the university sets the minimum ACT score at 20, what percent of the applicants will be accepted?

Answer 1

Answer:

A) See the picture

B) 14

C) 45%

Step-by-step explanation:

A) To create a histogram like the one on the picture you can use an online tool like socscistatistics where the number of classes is customizable

B) Because the question B and C have to be responded using a frequency table with 8 classes the answer is 14; the method of using cumulative frequency tables should only be considered as a way of estimation, that is because you obtain values that depend on your choice of class intervals. The way to get a better answer would be to use all the scores in the distribution

Pc1 = 100*(4/40) = 10

Pc2 = 100*(4/40) = 10

Pc3 = 100*(3/40) = 7.5

Pc4 = 100*(11/40) = 27.5

Pc5 = 100*(5/40) = 12.5

Pc6 = 100*(4/40) = 10

Pc7 = 100*(7/40) = 17.5

Pc8 = 100*(2/40) = 5

Pc8 + Pc7 + Pc6 + Pc5 + Pc4 + Pc3 + Pc2 = 90%

Therefore, From class 8 to class 2 is the top 90% of the applicants and the minimum score is 14.

C) Scores equal to or greater than 20 are from class 8 to class 5

Pc8 + Pc7 + Pc6 + Pc5 = 45%