Question 1204357: It is known that a certain hockey goalie will successfully make a save 86.23% of the time. Suppose that the hockey goalie attempts to make 10 saves. What is the probability that the hockey goalie will make at least 8 saves?
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Let X be the random variable which denotes the number of saves that are made by the hockey goalie. Find the expected value and standard deviation of the random variable.
E(X) =
~ \sigma =
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this appears to be a vinomial distribution type problem.
the mean is n * p
the standard deviation is sqrt(n * p * (1-p)
here is a reference showing how to to calculate mean and variance and standard deviation from the web.
the standard deviation is the square root of the variance.
https://socratic.org/questions/how-do-you-find-the-mean-variance-and-standard-deviation-of-the-binomial-distrib
in your problem, the number of attempts is 10 and the success rate (p) is .8623.
the failure rate (q) is 1 - .8623 = .1377
the mean is n * p = 10 * .8623 = 8.623
the variance is equal to sqrt(n * p * (1-p) = 10 * .8623 * .1377) = 1.1873871.
the standard deviation is square root of that = 1.089672933.
the probability of a binomial distribution formula is p(x) = p^x * q^(n-x) * c(n,x).
to find the probablity of at least 8 saves, you need to get the sum of p(8), p(9), and p(10).
p(8) = .8623^8 * .1377^2 * c(10,8) = .2608239592.
p(9) = .8623^9 * .1377^1 * c(10,9) = .3629605423.
p(10) = .8623^10 * .1377^0 * c(10,10) = .2272918487.
the sum is equal to 0.8510763502.
that's the probability he will make at least 8 saves out of 10 tries.
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