Question

It is known that a certain hockey goalie will successfully make a save 87.61% of the time. Suppose that the hockey goalie attempts to make 11 saves. What is the probability that the hockey goalie will make at least 9 saves?

  

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)=  
   σ=  

Answer 1

1)

Let, X be the random variable which denotes the number of saves that are made by the hockey goalie.

p = 87.61% = 0.8761 , n = 11

X follows Binomial distribution with p = 0.8731 and n = 11

We have to find P( x >= 9 )

P( x >= 9 ) = 1 - P( x <= 8 )

Using Excel,   =BINOMDIST( x , n , p, 1 )

P( x <= 8 ) = BINOMDIST( 8, 11, 0.8761, 1 ) = 0.14679

So, P( x >= 9) = 1 - 0.14679 = 0.85321

Probability that the hockey goalie will make at least 9 saves 0.85321

2)

E( X ) = np = 11* 0.8761 = 9.6371

$\sigma =\sqrt{np(1-p)}$

σ- v/11 * 0.8761 (1-0.8761) 1.0927