Question

Between the hours of 2am and 3am, three cars per minute pass a toll booth. This is true for all 7 days of the week

1. Find the probability that 8 or more cars pass the toll booth for the 2 minute period from 2:01 am through 2:02 am on a given Monday.

2. Find the probability that 8 or more cars pass the toll booth for the 2 minute period from 2:01 am through 2:02 am on a given Monday, AND that 8 or more cars pass the toll booth

Answer #1

1)

Cars pass per minute = 3

Cars pass per 2 minute = 3 *2 = 6

Mean/Expected number of events of interest: λ = 6

P(X=x) = e-λλx/x! |

X | P(X) |

0 | 0.0025 |

1 | 0.0149 |

2 | 0.0446 |

3 | 0.0892 |

4 | 0.1339 |

5 | 0.1606 |

6 | 0.1606 |

7 | 0.1377 |

P(x>=8) = 1 - [P(X=0) + P(X=1) +...........+P(X=7)]

= 1 - 0.7440

= **0.256**

2)

Here question after AND seems to be missing the information. If not, then it is same as above.

**Please revert back in case of any doubt.**

**Please upvote. Thanks in advance.**

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