SOLUTION: The probability is 0.62 that a high school valedictorian graduates from college as cum laude. a) Let X be the number of cum laude graduates out of a random sample of 5 high school

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Question 660390: The probability is 0.62 that a high school valedictorian graduates from college as cum laude.
a) Let X be the number of cum laude graduates out of a random sample of 5 high school valedictorians. Find the probability distribution of the random variable X.
b) What is the probability that in random sample of 5 valedictorians, 4 will graduate as cum laude?
c) What is the probability that among a random sample of 5 valedictorians at most 3 will graduate as cum laude?
d) What is the probability that among a random sample of 5 valedictorians at least one will graduate as cum laude?
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

probability is 0.62 that a high school valedictorian graduates from college as cum laude

P = nCx* p%5Ex%2Aq%5E%28n-x%29 where p and q are the probabilities of success and failure respectively. 

In this case p(cum laude)= .62 & q = .38  and n = 5

random sample of 5 valedictorians

P(x = 4) = 5C4%28.62%29%5E4%28.38%29%5E1

P(x  ≤ 3) = 1 - P(x=4) - P(x=5) = 1+-+5C4%28.62%29%5E4%28.38%29%5E1+-+5C5%28.62%29%5E5%28.38%29%5E0

P(x  ≥ 1) = 1 - P(0)= 1+-+5C0%28.62%29%5E0%28.38%29%5E5