This Question: 1 pt 1of15(O complete) This Quiz: 15 pts possible Question Help *

Question

This Question: 1 pt 1of15(O complete) This Quiz: 15 pts possible Question Help * The average income in a oertain region in 2013 was $70,000 per person per year. Suppose the standard deviation is $35,000 and the distribution is right-skewed Suppose we take a random sample of 100 residents of the regior. 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? What is the probability that the sample mean will be more than $3,500 away from the population mean? a Choose the correct answer below. A. O B. ° C. 0 D. No, it is not large enough because the sample size of 100 is not greater than 10% of the population. Yes, it is large enough because the sample size of 100 is greater than 25. Yes, it is large enough because the population standard deviation of 35,000 is larger than the sample size of 100. No, it is not large enough because the sample size of 100 is less than 250. t. The mean is Sand the standard error is Type integers or decimals. Do not round) C. The probabilty is© (Round to four decimal places as needed.) Click to select your answerls). 669,%20false)." This corse 29

Explanation / Answer

A) Option-B

B) mean = 70000

Standard error = 35000/sqrt(100) = 3500

C) P(X > 73500) = P((X - mean)/(SD/sqrt(n)) > (73500 - 70000)/(35000/sqrt(100))

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587

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