Answered

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Given a population mean of 53.7 with a standard deviation of 1.3 and a sample size

of 6, answer these questions:

Part A: What is the standard deviation of the sampling distribution of X? Show your

work. (5 points)

Part B: What does the sample size need to be if you want the standard deviation of

the sampling distribution of x to be 0.325? Show your work. (5 points) (10 points)

Sagot :

JeanaShupp

Answer: A. 0.4899 B. 14

Step-by-step explanation:

If X = random variable

then, the standard deviation of the sampling distribution of X = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

A.

GIven: [tex]\sigma= 1.2, \n= 6[/tex]

The standard deviation of the sampling distribution of X = [tex]\dfrac{1.2}{\sqrt{6}}=0.4899[/tex]

B. Let n be the sample size,

[tex]0.325=\dfrac{1.2}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=\dfrac{1.2}{0.325}\\\\\Rightarrow\ \sqrt{n}=3.69230769231\\\\\Rightarrow\ n= (3.69230769231)^2=13.6331360947\approx 14[/tex]

Hence, the required sample size = 14

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