Question

Scores for a common standardized college aptitude test are
normally distributed with a mean of 484 and a standard deviation of
100. Randomly selected men are given a Prepartion Course before
taking this test. Assume, for sake of argument, that the
Preparation Course has no effect on people's test scores.

If 1 of the men is randomly selected, find the probability that his
score is at least 520.1.

P(*X* > 520.1) =

Enter your answer as a number accurate to 4 decimal places.

If 15 of the men are randomly selected, find the probability that
their mean score is at least 520.1.

P(*x-bar* > 520.1) =

Enter your answer as a number accurate to 4 decimal places.

If the random sample of 15 men does result in a mean score of
520.1, is there strong evidence to support a claim that the
Preapartion Course is actually effective? (Use the criteria that
"unusual" events have a probability of less than 5%.)

- No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 520.1 if the Preparation Course has no effect.
- Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 520.1 if the Preparation Course has no effect.

Answer #1

a)

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

here mean= μ= | 484 |

std deviation =σ= | 100.0000 |

probability
=P(X>520.1)=P(Z>(520.1-484)/100)=P(Z>0.36)=1-P(Z<0.36)=1-0.6406=0.3594 |

b)

sample size =n= | 15 |

std error=σ_{x̅}=σ/√n= |
25.8199 |

probability
=P(X>520.1)=P(Z>(520.1-484)/25.82)=P(Z>1.4)=1-P(Z<1.4)=1-0.9192=0.0808 |

c)since probability is not less than 0.05:

No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 520.1 if the Preparation Course has no effect.

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