Question

1) A particular fruit's weights are normally distributed, with a mean of 678 grams and a standard deviation of 28 grams. If you pick 3 fruits at random, then 6% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

2)A population of values has a normal distribution with μ=190.6
and σ=4.4. You intend to draw a random sample of size n=147.

Find *P*_{75}, which is the score separating the
bottom 75% scores from the top 25% scores.

*P*_{75} (for single values) =

Find *P*_{75}, which is the mean separating the
bottom 75% means from the top 25% means.

*P*_{75} (for sample means) =

Answer #1

1)

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

here mean= μ= | 678 |

std deviation =σ= | 28.000 |

sample size =n= | 3 |

std error=σ_{x̅}=σ/√n= |
16.16581 |

for 3th percentile critical value of z= | -1.881 | ||

therefore corresponding value=mean+z*std deviation= | 647.5955~ 648 gram |

2) (for single values)

for 75th percentile critical value of z= | 0.674 | ||

therefore corresponding value=mean+z*std deviation= |
193.5678~ 193.6 |

(for sample means) :

std error=σ_{x̅}=σ/√n= |
0.3629 |

therefore corresponding value=mean+z*std deviation= |
190.8448~ 190.8 |

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