# Intro Into Statistics

**Topics:**Poisson distribution, Binomial distribution, Normal distribution

**Pages:**7 (779 words)

**Published:**January 13, 2013

Assume there are 23 homes in the Quail Creek area and 9 of them have a security system. Four homes are selected at random:|

(a)| What is the probability all four of the selected homes have a security system? (Round your answer to 4 decimal places.)|

Probability| |

(b)| What is the probability none of the four selected homes have a security system? (Round your answer to 4 decimal places.)|

Probability| |

(c)| What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)|

Probability| |

(d)| Are the events dependent or independent?|

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rev: 02-04-2011

Explanation:

(a)

0.0142, found by (9/23)(8/22)(7/21)(6/20)

(b)

0.1130, found by (14/23)(13/22)(12/21)(11/20)

(c)

0.8870, found by 1 − 0.1130

Exercise 5-37

An overnight express company must include thirteen cities on its route. How many different routes are possible, assuming that it matters in which order the cities are included in the routing?|

Number of different routes| |

Explanation:

6,227,020,800, found by 13!

Exercise 5-26

All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .73, the probability the second truck is available is .56, and the probability that both trucks are available is .46:|

What is the probability neither truck is available? (Round your answer to 2 decimal places.)|

Probability| |

Explanation:

0.17, found by (1 − 0.83)

Exercise 5-27

Refer to the following table.|

Second Event| First Event| |

| A1| A2| A3| Total|

B1| 3 | 4 | 6 | 13 |

B2| 3 | 5 | 5 | 13 |

Total| 6 | 9 | 11 | 26 |

(a)| Determine P(A3). |

P(A3) = | |

(b)| Determine P(B1|A1). |

P(B1|A1) =| |

(c)| Determine P(B1 and A2). |

P(B1 and A2) =| |

Explanation:

(a)

P(A3) = 11/26 = 0.42

(b)

P(B1|A1) = 3/6 = 0.50

(c)

P(B1 and A2) = 4/26 = 0.15

Exercise 6-9

In a binomial situation n = 5 and .40. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.)|

(a)| x = 3|

Probability| |

(b)| x = 4|

Probability| |

Explanation:

Exercise 6-52

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 3.3 emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.|

(a)| What is the probability Linda Lahey, company president, received exactly 2 emails between 4 P.M. and 5 P.M. yesterday? |

Probability| |

(b)| What is the probability she received 7 or more emails during the same period? |

Probability| |

(c)| What is the probability she received one or less email during the period? |

Probability| |

Explanation:

(a)

(b)

0.051 found by 0.0312 + 0.0129 + 0.0047 + 0.0016 + 0.0005 + 0.0001

(c)

0.1586 found by 0.0369 + 0.1217

Exercise 6-23

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports they can resolve customer problems the same day they are reported in 68 percent of the cases. Suppose the 15 cases reported today are representative of all complaints.|

(a-1)| How many of the problems would you expect to be resolved today? |

Number of Problems| |

(a-2)| What is the standard deviation? |

Standard Deviation| |

(b)| What is the probability 8 of the problems can be resolved today? |

Probability| |

(c)| What is the probability 8 or 9 of the problems can be resolved today? |

Probability| |

(d)| What is the probability more than 10 of the problems can be resolved...

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