Question

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

Answer 1

Answer: A. 0.4899 B. 14

Step-by-step explanation:

If X = random variable

then, the standard deviation of the sampling distribution of X = $\dfrac{\sigma}{\sqrt{n}}$

A.

GIven: $\sigma= 1.2, \n= 6$

The standard deviation of the sampling distribution of X = $\dfrac{1.2}{\sqrt{6}}=0.4899$

B. Let n be the sample size,

$0.325=\dfrac{1.2}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=\dfrac{1.2}{0.325}\\\\\Rightarrow\ \sqrt{n}=3.69230769231\\\\\Rightarrow\ n= (3.69230769231)^2=13.6331360947\approx 14$

Hence, the required sample size = 14