Question

10) A survey of business students who had taken the Graduate Management Admission Test (GMAT) indicated that students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400. Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400. It has been determined that 70% of the business students spent at least five hours reviewing for the test. a. Find the probability of scoring above 400. b. Find the probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.

Answer 1

Answer:

0.79 ; 0.753

Step-by-step explanation:

Given that:

Students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400 :

≥ 5 hours review = 0.85

Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400

< 5 hours = 0.65

70% (0.7) of business students spend atleast 5 hours review time

A.) probability of scoring above 400

(Proportion who spend atleast 5 hours review time * 0.85) + (Proportion who do not spend atleast 5 hours * 0.65)

Proportion who do not spend atleast 5 hours = (1 - proportion who spend atleast 5 hours) = 1 - 0.7 = 0.3

Hence,

P(scoring above 400) = (0.7 * 0.85) + (0.3 * 0.65) = 0.595 + 0.195

= 0.79

B.) probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.

P(spent ≥5 hours review | score above 400) :

P(spent ≥5 hours review) / P(score > 400)

(0.7 * 0.85) / 0.79

0.595 / 0.79

= 0.753