Question

USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take nine people at random off a city street. (a) Make a histogram showing the probability distribution of the number of illiterate people out of the nine people in the sample. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot Correct: Your answer is correct. (b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.) μ = people σ = people Find the expected number of people in this sample who are illiterate. (Round your answer to a whole number.) (c) How many people would you need to interview to be 98% sure that at least seven of these people can read and write (are not illiterate)? people

Answer #1

Ans:

a)

**P(x=k)=9C _{k}*0.2^{k}*0.8^{9-k}**

x | p(x) |

0 | 0.1342 |

1 | 0.3020 |

2 | 0.3020 |

3 | 0.1762 |

4 | 0.0661 |

5 | 0.0165 |

6 | 0.0028 |

7 | 0.0003 |

8 | 0.0000 |

9 | 0.0000 |

b)

Mean=np=9*0.2=**1.8**

standard deviation=sqrt(9*0.2*0.8)=**1.2**

c)

1-p=1-0.2=0.8 i.e. 80% can read and write

P(x>=7)=1-P(x<=6)

=1-binomdist(6,n,0.8,true)

n | P(x>=7) |

7 | 0.210 |

8 | 0.503 |

9 | 0.738 |

10 | 0.879 |

11 | 0.950 |

12 |
0.981 |

13 | 0.993 |

**n=12**

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