10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to
ID: 3330820 • Letter: 1
Question
10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to score 30% of the field goals. Assume she tries 15 field goals in a game. (a) Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (b) Find the probability that Mimi scores at least 3 of the 15 field goals. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.
Explanation / Answer
a) Number of trials, n = 15
Probability of successes, p = 0.3
Probability of failures,q = 1 - 0.3 = 0.7
b) P(X) = nCx px qn-x
P(at least 3 of 15) = 1 - P(X <3)
= 1 - P(0) - P(1) - P(2)
= 1 - 0.715 - 15x0.3x0.714 - 15C2x0.32x0.713
= 1 - 0.0047 - 0.0305 - 0.0916
= 0.873
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