Question

The record of an athlete shows that she scores 0.82 of the points she attempts to make. If she made 20 attempts, what is the probability that she scores 13 points? Express your answer as a decimal rounded to 4 places.

A) 0.6154
B) 0.6923
C) 0.7500
D) 0.8500

Answer 1

To find the probability, use the binomial probability formula with the given values of n, k, and p.

Step-by-step explanation:

To find the probability that the athlete scores 13 points out of 20 attempts with a success rate of 0.82, we can use the binomial probability formula.

The formula P(X=k) = C(n,k) * p^k * (1-p)^(n-k) can be used, where P(X=k) represents the probability of k successes, n represents the number of trials, p represents the probability of success in a single trial, and C(n,k) represents the number of combinations of n items taken k at a time.

In this case, n = 20, k = 13, and p = 0.82. Plugging these values into the formula, we get:

P(X=13) = C(20,13) * (0.82^13) * (0.18^7)

Calculating this expression, we find that the probability is approximately 0.6154, which corresponds to option A.