Question

(1 point) It is known that a certain hockey goalie will successfully make a save 91.75% of the time. Suppose that the hockey goalie attempts to make 15 saves. What is the probability that the hockey goalie will make at least 13 saves?

  

Let XX 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)=E(X)=  
   σ= σ=

Answer 1

1)

X ~ Bin ( n , p)

Where n = 15 , p = 0.9175

P(X) = ⁿC_X * p^X * ( 1 - p)^n-X

P(X >= 13) = P(X = 13) + P(X = 14) + P(X = 15)

= ¹⁵C₁₃ * 0.9175¹³ * ( 1 - 0.9175)² + ¹⁵C₁₄ * 0.9175¹⁴ * ( 1 - 0.9175) + ¹⁵C₁₅ * 0.9175¹⁵ * ( 1 - 0.9175)⁰

= 0.8789

b)

E(X) = np = 15 * 0.9175 = 13.7625

= sqrt ( n p ( 1 - p) )

= sqrt ( 15 * 0.9175 ( 1 - 0.9175))

= 1.0656