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Chapter 6: Q.26 (page 356)

Friends How many close friends do you have? An opinion poll asks this question of an SRS of 1100 adults. Suppose that the number of close friends adults claim to have varies from person to person with mean 渭=9 and standard deviation 蟽=2.5. We will see later that in repeated random samples of size 1100, the mean response x will vary according to the Normal distribution with mean 9 and standard deviation 0.075. What is role="math" localid="1649504967961" P(8.9鈮�x鈮�9.1), the probability that the sample result x estimates the population truth 渭=9 to within 卤0.1?

Short Answer

Expert verified

The probability ofP(8.9鈮�x鈮�9.1)is0.8164.

Step by step solution

01

Given Information

An opinion poll asks this question of an SRS of 1100 adults. Suppose that the number of close friends adults claim to have varies from person to person with mean 渭=9 and standard deviation 蟽=2.5.

02

Given Information

The sample mean is normally distributed with mean 渭and standard deviation 蟽/n.

Thez-score is the sample value multiplied by the standard deviation divided by the mean:

localid="1649915865099" z=x炉-渭蟽/n=8.9-92.5/1100鈮�-1.33

localid="1649915875646" z=x炉-渭蟽/n=9.1-92.5/1100鈮�1.33

Using the normal probability table in the appendix, calculate the corresponding probability:

localid="1649916024235" P(8.9鈮�x炉鈮�9.1)=P(-1.33<Z<1.33)=P(Z<1.33)-P(Z<-1.33)=0.9082鈭�0.0918=0.8164

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