Question

A random sample of size n = 100 is obtained from a population with fl= 300 and o= 50. Which of the following statements best describes the sampling distribution of Ž in terms of its shape, mean, and standard deviation? O The sampling distribution of is approximately normal withmean equal to 300 and standard deviation equal to 5. O The sampling distribution of is approximately normal withmean equal to 30 and standard deviation equal to 5. O The sampling distribution of is approximately normal withmean equal to 300 and standard deviation equal to 50. O The sampling distribution of is approximately normal withmean equal to 3 and standard deviation equal to 0.5. o none of the above

Answer 1

Solution :

Given that ,

mean = $\mu$ = 300

standard deviation = $\sigma$ = 50

n = 100

sample distribution of sample mean is ,

$\mu$$\bar x$ = $\mu$

$\mu$$\bar x$ = 300

sampling distribution of standard deviation

$\sigma$$\bar x$ =$\sigma$  / $\sqrt$ n =50 / $\sqrt$ 100=5

$\sigma$$\bar x$ = 5

sampling distribution is approximately normal with mean =300 and standard deviation =5