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Tju [1.3M]
4 years ago
15

A university claims that 80% of its basketball players get degrees. An investigation examines the fate of all 20 players who ent

ered the program over a period of several years that ended six years ago. Of these players, 11 graduated and the remaining 9 are no longer in school. If the university's claim is true, the number of players among the 20 who graduated should have the binomial distribution with n = 20 and p = 0.8. Use the binomial probability formula to answer the question, What is the probability that not all of the 20 graduate?
Mathematics
1 answer:
diamong [38]4 years ago
4 0

Answer:

The probability of not all players graduate in approximately 0.988.

Step-by-step explanation:

Let's define,

X = "Number of players that graduated"

We know that X \sim Bin(20;0.8) and the probability density function for a binomial random variable is:

P(X = k) = {20 \choose k}(0.8)^k(0.2)^{20-k}, with k \leq 20

We want to know the probability that not all of the 20 graduate, in other words we want to know the probability of P(X < 20).

P(X < 20) = 1 - P(X = 20) =\\= 1 - {20 \choose 20}(0.8)^{20}(0.2)^0 =\\= 1 - 0.8^{20} \approx 0.988

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