Answer:
a) The probability to select at least 9 graduated students is 0.8824
b) It is unusual to get 7 or less graduated students out of 10 randomly selected from the special program.
Step-by-step explanation:
a) Let X be the total amount of graduated students in the selection. X is a random variable with Binomial distribution B(10,0.94). The probability of X to be at least 9 is
Thus, the probability is 0.8824
b) Lets compute the probability of X being at most 7 (because it would be unusual to get few students). Note that
P(X ≤ 7) = 1-P(X > 7) = 1- (P(X=8) + P(X ≥9))
P(X≥9) was computed before, and
Thus,
P(X ≤ 7) = 1-(0.0986+0.8824) = 0.019 < 0.05
The probability to select 7 or less graduated students is 0.019, less than 2% of the cases. We can say that it is unusual.