Name 100717 9 Pts The mean height for a probability distrib

Name: 10/07/17 (9 Pts) The mean height, , for a probability distribution of heights is 65 inches and the standard deviation, o, is 3 inches. 4. a) If a random sample of 16 people is obtained from the above population, can the sampling distribution of sample means be assumed to have a normal distribution? Why or why not. b) If a random sample of 40 people is obtained from the above population, can the sampling distribution of sample means be assumed to have a normal distribution? Why or why not. c) If a normal probability distribution of heights is given, can the sampling distribution of sample be assumed to have a normal distribution? Why or why not. 5, (3 Pts) Suppose 1000, 95% confidence intervals, were obtained for a population mean, Approximately how many of the intervals are expected to contain ?

Solution

Answer:

4

a)

We know as for large sample size i.e. n > 30 , the sampling distribution of sample means assumed to be follows Normal distribution .

Here given that sample size is 16 which is small. Therefore sampling distribution of sample means does not follows Normal Distribution.

b)

Here given that sample size is 40 which is large. Therefore sampling distribution of sample means assumed to be follows Normal Distribution.

c)

Here given distribution of height is Normal. Therefore sampling distribution of sample means assumed to be follows Normal Distribution.

5) The interpretation of a 95% confidence interval for the mean is : If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.

Therefore here 950 of the intervals are expected to contain the population mean µ.