# Probability and Statistics

**Question description**

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Among U.S. cities with a population of more than 250,000 the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is in New York City, where the mean time is 38.8 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.7 minutes.

a. | What percent of the New York City commutes are for less than 27 minutes? |

Percent | % |

b. | What percent are between 27 and 35 minutes? |

Percent | % |

c. | What percent are between 27 and 43 minutes? |

Percent | % |

A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.70 minutes and the standard deviation was 0.60 minutes.

a. | What fraction of the calls last between 3.70 and 4.50 minutes? |

Fraction of calls |

b. | What fraction of the calls last more than 4.50 minutes? |

Fraction of calls |

c. | What fraction of the calls last between 4.50 and 5.50 minutes? |

Fraction of calls |

d. | What fraction of the calls last between 3.00 and 5.50 minutes? |

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