Problem 1
Answer: choice D) 84% of the wage earners earn less than $14,000 each
------------
The empirical rule states that 95% of the area under a normal curve is within 2 standard deviations (approximately), so 100-95 = 5% is found in the two tails combined, leaving 5/2 = 2.5% in each tail. Because the top 2.5% earns $18000 or more, this means 18000 is roughly 2 standard deviations above the mean, so z = 2
If z = 2 corresponds to with x = 18000, with mean mu = 10000, then the standard deviation sigma is...
z = (x-mu)/sigma
2 = (18000 - 10000)/sigma
2 = 8000/sigma
2sigma = 8000
sigma = 8000/2
sigma = 4000
So mu+sigma = 10000+4000 = 14000 is the cutoff mark for the earners 1 standard deviation above the mean.
Check out the attached image figue 1 for the diagram for the empirical rule. Add up the values that are to the left of z = 1, so 2.35+13.5+34+34 = 83.85 which rounds to 84
===============================================
Problem 2
Answer: choice D) 2.5%
-----------
x = 250, mu = 190 and sigma = 30
z = (x-mu)/sigma
z = (250-190)/30
z = 60/30
z = 2
According to the emprical rule, roughly 95% of the distribution is within 2 standard deviations. So 100-95 = 5% is in the combined tails leaving 5/2 = 2.5% is in the upper tail.
===============================================
Problem 3
Answer: Choice D) 4,4,4,5,5,6,7,7,8,8,8
------------
Plot each of the values on a dot plot. See the attached image figure 2 for each dotplot. Notice how plot D is bimodal with two hill features, so this distribution is non-normal. Normal distributions only have one mode (one hill).