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
