Question

The probability of obtaining a random sample mean which is lower than the population mean is

		1.00
		0
		.50
		none of these, since a sample mean can never be lower than a population mean

Answer 1

Solution:

The probability of obtaining a random sample mean which is lower than the population mean is

0.50

(3rd option is correct)

Explanation:

Solution:

Suppose be the population mean and be the population SD

Suppose that a sample of size n is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean =   

SD =      

Now ,

P( sample mean is lower than the population mean)

= P( < )

= P[( - )/ < ( - )/]

= P(Z < 0.00)  

= 0.50

Z is the standard normal variate. Use z table to find P(Z < 0.00)

Answer : 0.50