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• Pop Questions
• 7.4
• Test Friday-No 7.4 on it
• Homework
• Book Assignment 7
• Section 7.4, p. 488 - 2, 8(order doesnt
  matter), 13

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Pop Questions
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True or False

• 1. 68 of any data set lie within 1 standard
  deviation of the mean.
• 2. There is no way to determine if a data point
  is an outlier.

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(No Transcript)
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Other questions

• 3. When would it be impossible (or illogical) to
  use a pie chart?
• 4. How can we interpret the mean?

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Things get a little more complicated when you
start paying money for a game, and can get
various returns.

• A school is having a carnival to raise funds. In
  the following game, the player spins the spinner
  and receives the dollar amount on the which the
  spinner lands. If it costs 2 to play this game,
  in this a fair game?

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• How can we find our
• theoretical winnings?

8

• So we have that 1/8 of the time, well win 5
  1/8 of the time, well win 4 1/4 of the time,
  well win 2 and 1/2 of the time, well will
  nothing.
• Were using the concept of weighted averages.

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• Each piece is like a credit.
• So to find the average we do
• (0(4)2(2)4(1)5(1))/8
• 1.62
• So, per turn, on average we would win 1.62

0
5
0
2
0
2
4
0
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Is it then a fair game?
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13. Expected Value This is what we were finding
in the previous example.

• The term for the theoretical winnings per turn.
• Lets denote
• each even as E1, E2,, En
• the probability of each event as
• P1, P2,, Pn
• the payoff of each even as
• X1, X2,, Xn
• The expected value is then
• P1X1 P2 X2 Pn Xn
• A game is only fair if the expected value of the
  game equals the cost of playing the game.

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1. Hack-a-Shaq Source http//www.espn.go.com/nba
/teamstats?teamlal

• Shaquille O'Neal is one of the best players on
  the professional basketball team the Los Angeles
  Lakers.   Shaq, as he is nicknamed, stands 7' 1"
  tall and weighs 330 pounds.  Most of the shots he
  takes are close to the basket, and because he is
  so big other players have a hard time stopping
  him from making baskets.  In fact, he makes 57.2
  of  his shots, which is impressive given that
  most players make about 45.
• In basketball,  when a player trying to make a
  shot is hit on the body by someone on the
  opposing team, thereby causing the player to miss
  the shot, the player gets to take two free shots
  from 15 feet away from the basket.  These shots
  are called foul shots.   Shaq does not shoot foul
  shots very well.  In fact, he makes only 51.3 of
  his foul shots.
• Regular shots are worth two points.  Foul shots
  are worth one point each.
• Because Shaq is less likely to make foul shots,
  one strategy is to foul him whenever he touches
  the ball.  This strategy has been nicknamed the
  "hack-a-Shaq."  Let's see if the hack-a-Shaq pays
  off.

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Problems

• 1.  Calculate the expected value of the number of
  points Shaq scores on one regular shot (not foul
  shots) at the basket (i.e., he makes or misses
  the shot).   Regular shots are the ones he has a
  57.2 chance of making and are worth 2 pts.
• 2.  Assume that all foul shots are independent
  events (examinations of foul shooting records
  suggest this is approximately true).  Calculate
  the expected value of the number of points Shaq
  gets when he shoots two foul shots.
• 3.  Compare the EV for  foul shots to the EV for
  regular shots.   Based on these expected values,
  should opposing teams adopt the hack-a-Shaq?