Question

In each case, determine if the distribution of the sample mean (x-bar) is NORMALLY DISTRIBUTED, AT LEAST APPROXIMATELY NORMALLY DISTRIBUTED, or CANNOT BE DETERMINED.

The population is known to be normally distributed, the sample size is n = 56. a) can not be determined b) at least approximately distributed c)normally distributed.

The population distribution is not known, sample size is n = 100. a) can not be determined b) at least approximately distributed c)normally distributed.

The population is known to be normally distributed, sample size is n = 15. a) can not be determined b) at least approximately distributed c)normally distributed.

The population distribution is unknown, sample size is 15. a) can not be determined b) at least approximately distributed c)normally distributed.

Answer 1

Ans:

when sample size is sufficiently large i.e. n>=30,sampling distribution of sample means is normally distributed irrespective the shape of the population distribution.

When population distribution is normal,sampling distribution of sample means is normally distributed even if sample size is small.

1)The population is known to be normally distributed, the sample size is n = 56

Option c is correct.

normally distributed

2)The population distribution is not known, sample size is n = 100

Option c is correct.

normally distributed

3)The population is known to be normally distributed, sample size is n = 15

Option c is correct.

normally distributed

4)The population distribution is unknown, sample size is 15.

Option a is correct.

can not be determined