Answer? This Quiz: 15 pts pr 4 1 of 15 (0 complete) This Question: 1 pt Question

Question

Answer? This Quiz: 15 pts pr 4 1 of 15 (0 complete) This Question: 1 pt Question Help The average income in a certain region in 2013 was $75,000 per person per year suppose the standard deviation s s27000 and the distributonis nght ewed. Suppose we take a random sample of 100 residents of the region. 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? away from the population mean? c. What is the probability that the sample mean will be more than $2,700 a. Choose the correct answer below. O A. No, it is not large enough because the sample size of 100 is less than 250 O B. Yes, it is large enough because the sample size of 100 is greater than 25. the population. O C. No, it is not large enough because the sample size of 100 is not greater than 10% of Click to select your answer(s)

Explanation / Answer

A.a) Yes,it is large enough because sample size of 100 is greater than 25

A.b) Mean=75000

Standard error=27000/sqrt(100)=2700

A.c) As per central limit theorem,

68% of data falls within ±1SD of mean

hence from the probelm we say that 68% of values falls within ±2700 of mean

therefore the probability that sample mean will be more than 2700 from population is 0.32/2=0.16 or 16%

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