Question

Suppose the CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

(a)What is the probability that the mean price for a sample of 20 federal income tax returns is within $16 of the population mean? (Round your answer to four decimal places.)

(b)What is the probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean? (Round your answer to four decimal places.)

(c)What is the probability that the mean price for a sample of 121 federal income tax returns is within $16 of the population mean?(Round your answer to four decimal places.)

(d)Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to ensure at least a 0.95 probability that the sample mean is within $16 of the population mean? (Select all that apply.)

20 customers

60 customers

121 customers

none of the above

Answer #1

a)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 273 |

std deviation =σ= | 100.000 |

sample size =n= | 20 |

std error=σ_{x̅}=σ/√n= |
22.3607 |

probability = | P(257<X<289) | = | P(-0.72<Z<0.72)= | 0.7642-0.2358= |
0.5284 |

b)

std error=σ_{x̅}=σ/√n= |
12.9099 |

probability = | P(257<X<289) | = | P(-1.24<Z<1.24)= | 0.8925-0.1075= |
0.7850 |

c)

std error=σ_{x̅}=σ/√n= |
9.0909 |

probability = | P(257<X<289) | = | P(-1.76<Z<1.76)= | 0.9608-0.0392= |
0.9216 |

d)

none of the above :as probability is less than 0.95 in each of above 3 cases

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