# Suppose an x distribution has mean μ = 2. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.(a) What is the value of the mean of each of the two x distributions?For n = 49, μx =  For n = 81, μx =  (b) For which x distribution is P(x > 2.5) smaller? Explain your answer.The distribution with n = 49 because the standard deviation will be smaller.The distribution with n = 81 because the standard deviation will be smaller.    The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be larger.(c) For which x distribution is P(1.5 < x < 2.5) greater? Explain your answer.The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 49 because the standard deviation will be smaller.    The distribution with n = 81 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be smaller.

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Suppose an x distribution has mean μ = 2. Consider two corresponding

x

distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.

(a) What is the value of the mean of each of the two
x
distributions?
 For n = 49, μ x  = For n = 81, μ x  =

(b) For which
x
distribution is P(
x
The distribution with n = 49 because the standard deviation will be smaller.The distribution with n = 81 because the standard deviation will be smaller.    The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be larger.

(c) For which
x
distribution is P(1.5 <
x
The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 49 because the standard deviation will be smaller.    The distribution with n = 81 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be smaller.

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Step 1

Given
a)
x distribution has mean µ = 2
The mean of the sampling distribution is nothing but the population mean. So
for sample size n = 49 the mean µ = 2
for sample size n  = 81 the mean µ = 2

Step 2

b)
For x distribution P( x > 2.5)
The standard deviation is inversly proportional to sample size. As the sample size increases the standard deviatio...

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