Question
MATH 1342 21420 Homework: Section 9.2-The Central Limit Theorem for Sample M Score: 0 of 1 pt | 10 01 15 (9 complete) HW Score: 51 85%,778 of 15 9.2.13 The Suppose we take a random sample of 100 residents of the region. ncome in a certain region in 2013 was $67,000 per person per year. Suppose the standard deviation is $32 000 and the distribution is right ked a is the sample size large enough to use the Central Limit Theorem for means? Explain. b What are the mean and standard error of the sampling distribution? c. What i s the probability that the sample mean will be more than $3,200 away from the population mean? A. Yes, it is large enough because the sample size of 100 is greater than 25 OB No, it is not large enough because the sample size of 100 is less than 250 C. No, t is not large enough because the sample size of 100 is not greater than 10% of the population. D. Yes, it is large enough because the population standard deviation of 32,000 is larger than the sample size of 100 b The mean is $ and the (Type integers or decimals Do not round ) Enter your answer in the edit fields and then click Check Answer Clear Ail remaining
Explanation / Answer
(a) Yes, sample size is large enough because the sample size of 100 is greater than 25.
(b) Mean = $ 67000 per year
Standard error = / sqrt(n) = 32000 / sqrt(100) = 32000/10 = $ 3200
(c) Pr ( Sample mean > $32000 +- $ 3200 ; $32000 ; $3200)
here we can apply empirical rule.
Pr(Sample mean > +- ) = Pr( Z >1) + Pr(Z <-1) = 2 * 0.1587 = 0.3174
so, 31.74% probable.
