Question

1) A sample of size 25 is chosen from a population. Assume the probability distribution is normal. If the mean of the sample is 80 and the standard deviation is 6, find the lower bound of the 99% confidence interval. Round off to three decimal places.

2) A sample of size 36 is chosen from a population. The sample mean is 50 and the standard deviation is 5. Find the upper limit of the 95% confidence interval for the population mean. .Round off to three decimal places.

3) Light bulbs are found to have a mean life of 800 miles. The standard deviation is 50. A sample of 100 is chosen. Find the probability that

X < 795

4) A population has a mean of 60 and a standard deviation of 61. Samples of size 100 are randomly selected.

Calculate the standard deviation of the sample distribution of X. Round off to 3 decimal places.

5)Tires are found to have a mean life of 800 miles. The standard deviation is 50. A sample of 100 is chosen. Find the probability that

X < 795

Answer 1

Ans: D n=25 x=80, S = 6 for 99 do Confidence, af = 24 to Edlr idf Cool, 24 = 2.797 Lower bound x-te (S) = 80-2.797 / 6 325 80 - 3.3567 76.644 n=36 I = 50, S5 for 950o Confidence, 7.- 20.05-1.96 upper bonit x + Ze - 50 ± 1.96 15/36) = 151.633 2 M = 800 r = 50, n=100 P ( x L (795) - BLE X-M 795-800 olm 501 Noo = 10.15866 P/za-))

M=60, 5=61, n =100 standard devation of sample dostribution 61 6.100 of x Х 1100 5 M = 800 o=50, n=100 X-u < B (x-795). 795-800 50 15100 olin Plze-1) = (0.15B66