Suppose a random variable has population mean 140 and popula

Suppose a random variable has population mean -140 and population standard deviation 40. What is the upper value of the probability interval containing 95% of the sample means of sample size n = 100? (Round to 2 decimal places.)

Suppose a random variable has population standard deviation 25. What is the margin of error corresponding to the 95% confidence interval for sample a mean constructed from a sample of size 49? (Round to 2 decimal places.)

Solution

Answer:

Given population mean = 140 and population std dev= 40

Upper value of probability interval containing 95% of sample emans of n=100 can be found as:

X\' + Z ?/ sqrt(n)

= 140+ (1.96*40/10) = 140+7.84 = 147.84

b) Given population std dev=25

Given CI= 95%, size of sample= 49

Here margin of error E=1.96 * 25/ sqrt(49) = 1.96*25 / 7 = 7

Correct to 2 decimal places= 7.00