Question

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 39 and p = 0.18. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = , p̂ be approximated by a normal random variable because . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? , p̂ be approximated by a normal random variable because . (c) Suppose n = 61 and p = 0.26. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = , p̂ be approximated by a normal random variable because . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ =

Answer #1

a)

np= | 7.02 |

n(1-p)= | 31.98 |

p̂ be approximated by a normal random variable because np and nq >=5

here population proportion= μp= | 0.180 |

std error of proportion=σp=√(p*(1-p)/n)= | 0.062 |

b)

np= | 3.75 |

n(1-p)= | 21.25 |

p̂ cannot be approximated by a normal random variable because np <5

c)

np= | 15.86 |

n(1-p)= | 45.14 |

p̂ be approximated by a normal random variable because np and nq >=5

here population proportion= μp= | 0.260 |

std error of proportion=σp=√(p*(1-p)/n)= | 0.056 |

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