Question

D8: The following table of data represents the scores received on the 2015 SAT Mathematics Test, by gender. For each of the circumstances below, explain (don't just compute) how you would find these probabilities and what rule you applied to calculate them.

A)If a test taker is randomly selected, what is the probability that the test taker is male?

B)If a test taker is randomly selected, what is the probability that the test taker scored between 400 and 690?

C)If a test taker is randomly selected, what is the probability that the test taker is female or scored 700-800?

Score Range	Male	Female
200-290	33,987	31,462
300-390	121,664	142,491
400-490	242,281	297,876
500-590	230,577	265,340
600-690	127,109	130,075
700-800	39,184	36,475

Please provide detail how each answer is found.

Answer 1

We first obtain the sum of rows and columns here as:

Score Range	Male	Female	Total
200-290	33,987	31,462	65,449
300-390	1,21,664	1,42,491	2,64,155
400-490	2,42,281	2,97,876	5,40,157
500-590	2,30,577	2,65,340	4,95,917
600-690	1,27,109	1,30,075	2,57,184
700-800	39,184	36,475	75,659
Total	7,94,802	9,03,719	16,98,521

a)  If a test taker is randomly selected, the probability that the test taker is male is computed here as:

= n(Total Males) / n(Grand Total)

= 7,94,802 / 16,98,521

= 0.4679

Therefore 0.4679 is the required probability here.

b) If a test taker is randomly selected, the probability that the test taker scored between 400 and 690 is computed here as:

= n(test taker scored between 400 and 690) / n(Grand Total)

= (540157 + 495917 + 257184) / 16,98,521

= 0.7614

Therefore 0.7614 is the required probability here.

c) If a test taker is randomly selected, the probability that the test taker is female or scored 700-800 is computed here as:

= n(female or scored 700-800) / n(Grand Total)

= n(Female) + n(Scored 700-800 and Male) / n(Grand Total)

= (903719 + 39184) / 16,98,521

= 0.5551

Therefore 0.5551 is the required probability here.