Question

Identify the parameters p and n in the following binomial distribution scenario. Jack, a bowler, has a 0.38 probability of throwing a strike and a 0.62 probability of not throwing a strike. If Jack bowls 20 times, he wants to know the probability that he throws more than 10 strikes. (Consider a strike a success in the binomial distribution.)

Answer 1

Answer:

p = 0.38, n = 20

The probability that he throws more than 10 strikes = 0.09233

Step-by-step explanation:

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of times Jack wants to bowl = 20

x = Number of successes required = number of strikes he intends to get

p = probability of success = probability that Jack throws a strike = 0.38

q = probability of failure = probability that Jack doesn't throw a strike = 0.62

P(X > x) = Σ ⁿCₓ pˣ qⁿ⁻ˣ (summing from x+1 to n)

P(X > 10) = Σ ²⁰Cₓ pˣ qⁿ⁻ˣ (summing from 11 to 20)

P(X > 10) = [P(X=11) + P(X=12) + P(X=13) + P(X=14) + P(X=15) + P(X=16) + P(X=17) + P(X=18) + P(X=19) + P(X=20)

P(X > 10) = 0.09233

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