The starting baseball player has an average of a 0.250 probability of hitting th

Question

The starting baseball player has an average of a 0.250 probability of hitting the ball in a single "at bat". In one game, the player gets a total of 6 "at bats."

Let X be the number of hits the baseball player gets. It is already known that the distribution of X is a binomial probability distribution.

(a) What is the number of trials (n)

(b) What is the probability of successes (p)

(c) What is the probability of failures (q)

(d) Find the probability of at least 4 hits in the one game. (Round the answer to 3 decimal places) Show work for ALL answers.

Explanation / Answer

a) Number of trials, n = 6

b) Probability of successes, p = 0.25

c) Probability of failures, q = 1 - p

= 1 - 0.25

= 0.75

d) P(X) = nCx px qn-x

P(at least 4 hits) = P(4) + P(5) + P(6)

= 6C4x0.254x0.752 + 6x0.255x0.75 + 0.256

= 0.033 + 0.004 + 0.000

= 0.037

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