## Tuesday, November 16, 2010

### Chapter 6 Q18

Chapter 6 Q18

Let’s use Excel for this question...although the answers in the book use z scores.

a. At least \$40. Recall that Excel sums the probability from left to right, and we want the segment to the right of \$40. So go

=1-normdist(40,30,8.2,true) = 0.111

b. No higher than \$20. Now we want the segment to the left of \$20, so go

=normdist(20,30,8.2,true)=0.111

Now, you may have noticed that the two answers are the same! Well, pretty weird if they weren’t....because this is a normal distribution which is by definition symmetric. The mean is bang in the middle between 20 and 40, so of course the little ‘tails’ either side are the same area.

c. Now we want to know the value of the random variable ‘x’ that creates an area of 10% to the right of it? (Top 10%....) Use norminv for this, but recall that Excel sums from left to right. So go

=norminv(0.9,30,8.2)=40.51. That’s how high the stock price would have to be. See sketch below