Discrete Probability Distribution Solutions

Practicing material for Quiz #5 – Discrete Probability Distribution SOLUTIONS

1. The manager of a baseball team has determined that the number of walks, x, issued in a game by one of the pitchers is described by the probability distribution given below.

1. This pitcher issues as few as 0 walks and as many as 5 walks in a game.

1. Determine the following probabilities

i. P(x = 2) = 0.15

ii. P(x > 4) = 1 – 0.10 = 0.90

iii. P(x > 5) = 0

iv. P(2 < x < 4) = 0.15+0.45+0.15 = 0.75

1. Calculate the mean for this discrete probability distribution, µ = 2.85 walks

µ = Sxp(x) = 0(0.05) + 1(0.10) + 2(0.15) + 3(0.45) + 4(0.15) + 5(0.10) = 2.85

1. The average, over time, of walks issued in a game by one of the pitchers is 2.85 walks.

For the following binomial problems, in addition to the values of n and p, identify using words as to what n and p represent in terms of the problem. Use the binomial formula P(x = r) = _nC_r(p^r)(q^n-r) or tables to solve these problems.

1. It has been reported that about 25% of all resumes contain a major fabrication (Boston Sunday Globe, 1997)
   1. Find the probability that exactly 5 out of 18 randomly selected resumes contain a major fabrication.

n = 18 resumes

p = 0.25 = probability a resume contains a major fabrication

P(x = 5) = ₁₈C₅(0.25⁵)(0.75¹³) = 0.1988

1. Used the formula to solve the problem because p = 0.25 not in table.

1. Sixty percent of voters in a town oppose a proposed development. Find the following requested probabilities for the number of voters who oppose the development in a random sample of 18 voters; be sure to indicate n and p below. n = 18 voters p = 0.6 = probability a voter opposes the development in town

For each of the following, insert a relational symbol for the “?” and compute the requested probability. USED table

1. P(exactly 10) = P(x = 10) = 0.1734

1. P(more than 13) = P(x > 13) = 0.0614 + 0.0246 + 0.0069 + 0.0012 + 0.0001 = 0.0942