# Discrete Probability Distribution Solutions

Classified in Mathematics

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## 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.

x | p(x) |
---|---|

0 | 0.05 |

1 | 0.10 |

2 | 0.15 |

3 | 0.45 |

4 | 0.15 |

5 | 0.10 |

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

- 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**

- 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

**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) = _{n}C_{r}(p^{r})(q^{n-r}) or tables to solve these problems.

- It has been reported that about 25% of all resumes contain a major fabrication (Boston Sunday Globe, 1997)
- 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) = _{18}C_{5}(0.25^{5})(0.75^{13}) = **0.1988**

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

- 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

- P(exactly 10) = P(x = 10) =
**0.1734**

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