Answers to the Second Midterm Yellow Form
1. Box Average = -.4 so the expected value is 100 x -.4 = -$40
Solution for box average :
(-10 * .1) + (+2 * .3) + (0 * .6) = -.4
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)
-10 (if you picked an green one)
+2 (if you picked a brown one)
60% of the M&Ms are worth zero dolalrs
10% are worth -$10
30% are worth +$2
So, treat the M&M outcomes like a list of numbers, that is:
0, 0, 0, 0, 0, 0, -10, 2, 2, 2
The SD of this list is $3.3226
So the SE of the sum is root(100) * 3.3226 or $33.226
2. You lost $100, this is -100 and you were only expecting
to lose $40 (-40). Need to calculate Z to find the chance
of seeing this kind of outcome:
Z = -100 - (-40)
------------
33.226
= -1.81, round down to -1.80, the area to left of -1.80 is
3.595%. So there was about a 3.6% chance of losing $100 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 * (root(49)*2)/49))
5. Here, the population is known and you're being asked about the
chance of seeing a particular sample outcome -- specifically
between 10% and 14%.
Need a Z score
Z = 10% - 15%
------------------------------------- = -.28 or about -.25
(root 100) * (root .15 * .85)
------------------------ * 100
100
Z = 14% - 15%
------------------------------------- = -1.40
(root 100) * (root .15 * .85)
------------------------ * 100
100
The area associated with a Z = -1.40 is 83.85%
The area associated with a Z = -.25 is 19.74%
Take the difference in this case and divide by 2 to give
32.055%
6. C -- accuracy is determined by sample size not by
population size. See chapter 20.
7. E
8. it would be
35% + or - 4.77% (2 times the answer from #7)