Answers to the Second Midterm Green Form
1. Box Average = -.5 so the expected value is 100 x -.5 = -$50
Solution for box average :
(-20 * .1) + (+5 * .3) + (0 * .6) = -.5
SD of the box -- this is trickier. Remember the formula from
chapter 4? The standard deviation is the average deviation
of each outcome from the average. So we know the average is -.4
the possible outcomes are
0 (if you picked a red, yellow, orange, blue)
-20 (if you picked an green one)
+5 (if you picked a brown one)
60% of the M&Ms are worth zero dolalrs
10% are worth -$20
30% are worth +$5
So, treat the M&M outcomes like a list of numbers, that is:
0, 0, 0, 0, 0, 0, -20, 5, 5, 5
The SD of this list is $6.8739
So the SE of the sum is root(100) * 6.8739 = $68.739
2. You lost $191, this is -191 and you were only expecting
to lose $50 (-50). Need to calculate Z to find the chance
of seeing this kind of outcome:
Z = -191 - (-50)
------------
68.739
= -2.05, the area to left of -2.05 is
2.02%. So there was about a 2.0% chance of losing $191 or
more.
3. The newspaper is. Why? Because it uses a probability method
to generate a representative sample of the US population. The TV
method is biased -- selection bias and possibly reponse bias.
4. Answer is 13.4 to 14.6 hours. If you chose to
write 14/24 as the percentage of hours, it was OK only
if you contined and calculated the SE correctly (SE of
a percentage). Otherwise, the solution is:
14 hours + or - (2 * (2/(root 49)))
5. Here, the population is known and you're being asked about the
chance of seeing a particular sample outcome -- specifically
between 5% and 9%.
Need a Z score
Z = 9% - 10%
------------------------------------- = -.33 or about .30
(root 100) * (root .10 * .90)
------------------------ * 100
100
Z = 5% - 10%
------------------------------------- = -1.67 or about -1.65
(root 100) * (root .10 * .90)
------------------------ * 100
100
The area associated with a Z = -1.65 is 90.11%
The area associated with a Z = -.33 is 23.58%
Take the difference in this case and divide by 2 to give
33.265
6. C -- accuracy is determined by sample size not by
population size. See chapter 20.
7. E
8. it would be
75% + or - 4.33% (2 times the answer from #7)