Solve the following:

3. The heights, x cm of a large population of adults have a mean of 170 am and a standard deviation of II cm. random samples of size 15 were collected and in each sample the cample mean x ( in cm ) was calculated Find the meand and variance of x. 4. ) Suppose a random sample of size 400 I's taken from a population with a mean of too kq and standard deviation of 20 Kq If it is required to reduce the standard (eer) error of the mean to less than 0. 10 kq , what I's the minimum sample size ? 5.) Find the probability that the sample mean 49 lies between 47-5 and 48.5DATE QUIZ 2 SAMPLING DISTRIBUTION OF THE SAMPLE MEAN Consider the population 1 1, 4, 139 . Find the following : a_ population mean b: 3 sample means from $1.4, 133 e - Which gives a better estimate of the population mean ? Explain your answer 2) Suppose a teacher gave an ten-points quiz to the Grade II which compose of four students. The results of the quiz were 3, 5, 7, 9. For the cake of discussion, assume that the four students constitute the population. Find the following . a - population mean b - variance of the population c . If all samples of size 2 are taken with replacement from the scores of the four students , find the mean of each ample. (use table to represent the combination from 3 5, 7 9 and the sample mean ) . d. Create a frequency distribution of sample meant bared on your answer in letter e . Make a graph of the frequency distribution of sample means . f . Find the mean of the sample means g . Find the variance of sample means