Question 629065
Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.
a. Describe the shape of the sampling distribution of the sample mean x-bar.
Approaching normal.
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Do we need to make any assumptions about the shape of the population? Why or why not?
Ans: Independence of the data.
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b. Find the mean and the standard deviation of the sampling distribution of the sample mean x-bar.
mean of the sample means = mean of the population
std of the sample means = s/sqrt(n)
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c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P(x bar>21). Hint: Find the z value corresponding to 21 by using ?, and ? because we wish to calculate a probability about x-bar. Then sketch the sampling distribution and the probability.
z(21) = (21-20)/(4/sqrt(64)) = 1/(1/2) = 2
P(x-bar < 21) = P(z < 2) = 0.9772
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d. Calculate the probability that we will obtain a sample mean less than 19.385; that is, calculate P(x bar <19.385).
z(19.385) = (19.385-20)/[4/8] = 0.385/0.5 = 0.77
P(x bar <19.385) = P(z < 0.77) = 0.7794
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Cheers,
Stan H.
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