Question

g 5 points It is known that a certain lacrosse goalie will successfully make a save 80% of the time. (Assume that all save attempts are independent.) Suppose that the lacrosse goalie attempts to make 12 saves. (Round answers to three decimal places.) (a) What is the probability that the lacrosse goalie will make at least 10 saves

Answer 1

The probability that the lacrosse goalie will make at least 10 saves is 0.558.

Explanation:

Let X denote the number of saves the lacrosse goalie will successfully make.

It is provided that the probability of the lacrosse goalie making a successfully save is, p = 0.80.

It is assumed that all save attempts are independent.

Suppose that the lacrosse goalie attempts to make n = 12 saves.

The random variable X follows a binomial distribution with parameters n = 12 and p = 0.80.

Compute the probability that the lacrosse goalie will make at least 10 saves as follows:

`P(X\geq10 )=P(X=10)+P(X=11)+P(X=12)`

`={12\choose 10}(0.80)^(10)(0.20)^(2)+{12\choose 11}(0.80)^(11)(0.20)^(1)+{12\choose 12}(0.80)^(12)(0.20)^(0)\\\\=0.2835+0.2062+0.0687\\\\=0.5584\\\\\approx 0.558`

Thus, the probability that the lacrosse goalie will make at least 10 saves is 0.558.