Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 131 millimeters, and a standard deviation of 8 millimeters. If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3 millimeters? Round your answer to four decimal places.

Answer #1

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

here mean= μ= | 131 |

std deviation =σ= | 8.000 |

sample size =n= | 50 |

std error=σ_{x̅}=σ/√n= |
1.13137 |

probability that the sample mean would differ from the population mean by more than 3 millimeters:

probability
=1-P(128<X<134)=1-P((128-131)/1.131)<Z<(134-131)/1.131)=1-P(-2.65<Z<2.65)=1-(0.996-0.004)=0.0080 |

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