Question

Suppose a simple random sample of size n=81 is obtained from a population with mu=89 and sigma=27.

(a) Describe the sampling distribution of x overbar.

(b) What is P(x overbar > 92.9)?

(c) What is P( x overbar < or equals 82.7)?

(d) What is P(86 < x overbar < 96.35)?

Answer #1

a) sampling distribution of x overbar follows normal distribution from central limit thoerum as sample size n is greater than 30

here mean of sampling distribution =89

and standard deviation of sampling distribution of means =27/sqrt(81)=3

b)

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

probability = | P(X>92.9) | = | P(Z>1.3)= | 1-P(Z<1.3)= | 1-0.9032= |
0.0968 |

c)

probability = | P(X<82.7) | = | P(Z<-2.1)= | 0.0179 |

d)

probability = | P(86<X<96.35) | = | P(-0.3<Z<0.74)= | 0.7704-0.3821= | 0.3883 |

( please try 0.3892 if this comes wrong)

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