Question

Let the random variable X follow a Normal distribution with
variance σ^{2} = 625.

A random sample of n = 50 is obtained with a sample mean, X-Bar of 180.

What is the probability that μ is between 198 and 211?

What is Z-Score1 for μ greater than 198?

Answer #1

Table in MS-Excel | |

sigma2= | 625 |

sigma= | 25 |

sqrt(2)= | 1.414214 |

n | 50 |

sqrt(n)= | 7.071068 |

xbar | 180 |

xbar-198 | -18 |

xbar-211 | -31 |

(xbar-198)/(sigma/sqrt(n)) | -5.09117 |

(xbar-211)/(sigma/sqrt(n)) | -8.76812 |

P(Z<-8.768124) | 9.08E-19 |

P(Z<-5.091169) | 1.78E-07 |

ROUND(NORMSDIST(-8.768124),1) |
0 |

ROUND(NORMSDIST(-5.091169),1) |
0 |

In general,a z-score indicates how many standard deviations an element is from the mean. It can be calculated from the following formula: z = (X - μ) / σ

where, z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.

For
Questions 6 - 8, let the random variable X follow a Normal
distribution with variance σ2 = 625.
Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is
the probability that population mean μ is greater than 190?
a.
What is Z-Score for μ greater than 190 ==>
b.
P[Z > Z-Score] ==>
Q7. What
is the probability that μ is between 198 and 211?
a. What
is Z-Score1 for...

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