Question

The weight of potato chips in a largelarge-size bag is stated to be 16 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 16.3 ounces and a standard deviation of 0.17ounces. a) What fraction of all bags sold are underweight? b) Some of the chips are sold in "bargain packs" of 3 bags. What's the probability that none of the 3 is underweight? c) What's the probability that the mean weight of the 3 bags is below the stated amount? d) What's the probability that the mean weight of a 30-bag case of potato chips is below 16 ounces?

Answer #1

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

here mean= μ= | 16.3 |

std deviation =σ= | 0.170 |

a)

probability
=P(X<16)=(Z<(16-16.3)/0.17)=P(Z<-1.76)=0.0392 |

b)

probability that none of the 3 is underweight
=(1-0.0392)^3=**0.8869**

c)

sample size =n= | 3 |

std error=σ_{x̅}=σ/√n= |
0.09815 |

probability
=P(Xbar<16)=(Z<(16-16.3)/0.098)=P(Z<-3.06)=0.0011 |

d)

sample size =n= | 30 |

std error=σ_{x̅}=σ/√n= |
0.03104 |

probability
=P(X<16)=(Z<(16-16.3)/0.031)=P(Z<-9.67)=0.000 |

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