Question

A population of values has a normal distribution with μ = 53.9 and σ = 71.9 . You intend to draw a random sample of size n = 168 . Find the probability that a single randomly selected value is between 39.5 and 70. P(39.5 < X < 70) = Find the probability that a sample of size n = 168 is randomly selected with a mean between 39.5 and 70. P(39.5 < M < 70) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer #1

1)

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

here mean= μ= | 53.9 |

std deviation =σ= | 71.900 |

probability that a single randomly selected value is between 39.5 and 70:

probability = | P(39.5<X<70) | = | P(-0.2<Z<0.22)= | 0.5886-0.4206= | 0.1680 |

2)

sample size =n= | 168 |

std error=σ_{x̅}=σ/√n= |
5.5472 |

probability that a sample of size n = 168 is randomly selected with a mean between 39.5 and 70:

probability = | P(39.5<X<70) | = | P(-2.6<Z<2.9)= | 0.9981-0.0047= | 0.9934 |

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