10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to
ID: 3324876 • Letter: 1
Question
10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to score 20% of the field
goals. Assume she tries 10 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 10 field goals. (round the answer to 3 decimal
places) Show all work. Just the answer, without supporting work, will receive no credit.
Explanation / Answer
Pr(Able to score field goals) = 0.20
Number of trial goals n = 10
(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?
The Number of trials (n) = 10
Probability of success = 0.2
Probability of failure (q) = 0.8
(b) Find the probability that Mimi scores at least 3 of the 10 field goals.
Answer : Let say X is the number of field goals scored out of 10.
Pr(X >=3) = BIN ( X> = 3; 10 ; 0.2) = 1- BIN (X< 3; 10 ; 0.2)
BIN (X< 3; 10 ; 0.2) = 10C0 (0.2)0(0.8)10 + 10C1 (0.2)1 (0.8)9 + 10C2(0.2)2(0.8)8 =
= 0.1074 + 0.2684 + 0.302
= 0.6778
Pr(X >=3) = BIN ( X> = 3; 10 ; 0.2) = 1- BIN (X< 3; 10 ; 0.2) = 1- 0.6778 = 0.3222
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