Tuesday, July 15, 2008

6:53 PM: John Beck(Ins) has entered the room.
6:53 PM: John Beck(Ins): Hi, Bill
7:00 PM: Julius Uwansc has entered the room.
7:00 PM: John Beck(Ins): Hi, Julius!
7:00 PM: Julius Uwansc: Hi Prof
7:00 PM: John Beck(Ins): How are things back in Baltimore?
7:01 PM: Julius Uwansc: the weather id good
7:01 PM: John Beck(Ins): It's good out here too. Sunny and not too hot!
7:01 PM: Julius Uwansc: right now am in DC where i work
7:02 PM: John Beck(Ins): My son works in DC.
7:02 PM: John Beck(Ins): Near Dupont Circle.
7:02 PM: Julius Uwansc: Where in DC?
7:02 PM: John Beck(Ins): Where do you work?
7:02 PM: Julius Uwansc: its very close to my office that is 1700 Penn near w/house
7:03 PM: Julius Uwansc: I work for a law firm
7:03 PM: John Beck(Ins): My son works for an insurance company that insures US interests overseas.
7:04 PM: Julius Uwansc: thats a very good job for him
7:04 PM: John Beck(Ins): He loves to travel, so it's great!
7:04 PM: John Beck(Ins): Julius, it might be just the two of us, so let's get started.
7:04 PM: Julius Uwansc: i like to interact with others
7:04 PM: Julius Uwansc: ok
7:04 PM: John Beck(Ins): Let me know when you are on Ch 10_p1, please.
7:05 PM: Julius Uwansc: ok
7:05 PM: Jennifer Ann Johnson has entered the room.
7:05 PM: John Beck(Ins): Hi, Jennifer!
7:05 PM: John Beck(Ins): Jennifer, we are on Ch 10 P1.
7:05 PM: Jennifer Ann Johnson: Good Evening
7:06 PM: Julius Uwansc: hi Jenn
7:06 PM: John Beck(Ins): Go to page 2, please.
7:06 PM: Jennifer Ann Johnson: Hello Julius
7:06 PM: John Beck(Ins): It's handy to have a graph. A picture is worth a thousand words.
7:06 PM: John Beck(Ins): Go to page 3, please.
7:07 PM: John Beck(Ins): As you can probably see, when a distribution is "skewed right" it is because the mean is to the right of the median.
7:07 PM: John Beck(Ins): Can you guess when a distribution is "skewed left?"
7:07 PM: Julius Uwansc: when it is to the left
7:08 PM: John Beck(Ins): RIGHT
7:08 PM: John Beck(Ins): Go to page 4, please.
7:08 PM: Julius Uwansc: am on 4
7:08 PM: John Beck(Ins): Remember, I don't quiz on vocabulary, but I do use these words, so you should be familiar with them.
7:08 PM: John Beck(Ins): Go to page 5, please.
7:09 PM: John Beck(Ins): Notice that we have very few Cs, but lots of As and Fs.
7:09 PM: Jennifer Ann Johnson: I see
7:09 PM: John Beck(Ins): Go to page 6, please.
7:09 PM: Julius Uwansc: ok
7:10 PM: John Beck(Ins): We'll spend the rest of Chapter 10 and Chapter 11 talking about "Normal Distributions."
7:10 PM: John Beck(Ins): You might have called this type distribution as a "bell shapped curve."
7:10 PM: Jennifer Ann Johnson: Sounds familiar
7:10 PM: John Beck(Ins): Or you might have referred to a "bell curve."
7:10 PM: Julius Uwansc: no
7:10 PM: John Beck(Ins): Go to page 7, please.
7:11 PM: Julius Uwansc: on 7 now
7:11 PM: John Beck(Ins): For example, suppose the mean is 50 and the standard deviation is 10.
7:11 PM: John Beck(Ins): Then 50 + 10 = 60
7:11 PM: John Beck(Ins): And 50 - 10 = 40
7:11 PM: John Beck(Ins): So Approximately 68% of the scores will be between 40 and 60.
7:12 PM: Julius Uwansc: ok
7:12 PM: John Beck(Ins): By the way, to prove this we'd have to take 3 semesters of Calculus. We'll take their word for this.
7:12 PM: Jennifer Ann Johnson: How do you get 68%?
7:12 PM: John Beck(Ins): From calculus, Jenn.
7:12 PM: Jennifer Ann Johnson: I'll take your word for it :-)
7:13 PM: John Beck(Ins): It's been a long time, so I'll take their word also.
7:13 PM: Julius Uwansc: don't scare me
7:13 PM: John Beck(Ins): Go to page 8, please.
7:14 PM: John Beck(Ins): Remember, last week we had Chebyshev's Theorem. His theorem worked for any distribution. This works only for "normal distributions."
7:14 PM: John Beck(Ins): Go to page 9, please.
7:14 PM: John Beck(Ins): You don't have to memorize these values, Class. We're going to give you a table that has these values plus a lot more.
7:14 PM: John Beck(Ins): Go to page 10, please.
7:14 PM: Jennifer Ann Johnson: weee
7:15 PM: Meghan Wheeler has entered the room.
7:15 PM: Julius Uwansc: ok
7:15 PM: John Beck(Ins): Hi, Meghan!
7:15 PM: Meghan Wheeler: heoll sorry I'm late
7:15 PM: John Beck(Ins): Meghan, we're on Ch 10 p. 10.
7:15 PM: John Beck(Ins): No problem, Methan.
7:15 PM: Meghan Wheeler: thanks!
7:15 PM: John Beck(Ins): Meghan.
7:15 PM: John Beck(Ins): Let's click on Tools, then Table, please.
7:16 PM: John Beck(Ins): Do you see the shaded region of the normal curve?
7:16 PM: Jennifer Ann Johnson: yes
7:16 PM: Julius Uwansc: yes
7:16 PM: Meghan Wheeler: yes
7:17 PM: John Beck(Ins): This table will give us the area under the normal curve (the shaded region) for values between 0 and z.
7:17 PM: John Beck(Ins): For example, for z = .12, we see that A = .048
7:17 PM: John Beck(Ins): Okay?
7:17 PM: Jennifer Ann Johnson: Got it
7:17 PM: Meghan Wheeler: working on it
7:17 PM: Julius Uwansc: ok
7:18 PM: John Beck(Ins): What is A for z = 1.10?
7:18 PM: Meghan Wheeler: .364
7:18 PM: John Beck(Ins): RIGHT
7:18 PM: John Beck(Ins): Okay, Julius and Jenn?
7:19 PM: Jennifer Ann Johnson: Yes,
7:19 PM: Julius Uwansc: am looking
7:19 PM: John Beck(Ins): For the time being, we'll just have the shaded region and some mysterious value, z.
7:20 PM: John Beck(Ins): Okay, let's click on "Hide 'em"
7:20 PM: John Beck(Ins): Here we have a normal curve and we've shaded the region between z = 0 and z = 1.2
7:21 PM: John Beck(Ins): We can use the table to deterimine the fraction of the scores that lie within that region.
7:21 PM: Julius Uwansc: ok
7:21 PM: John Beck(Ins): What is the value for A?
7:21 PM: Jennifer Ann Johnson: .385 for z = 1.2
7:21 PM: John Beck(Ins): RIGHT
7:22 PM: John Beck(Ins): Do you see where she got .385?
7:22 PM: Meghan Wheeler: yes
7:22 PM: John Beck(Ins): So 38.5% of the scores are in the shaded region.
7:22 PM: John Beck(Ins): Go to page 11, please.
7:22 PM: John Beck(Ins): Go to page 12, please.
7:23 PM: John Beck(Ins): This time I have a value for z that is negative.
7:23 PM: Jennifer Ann Johnson: A = .209
7:23 PM: John Beck(Ins): Because of the symmetry of the normal curve, we can use z = .55 for z = -0.55
7:23 PM: John Beck(Ins): Right, Jenn!
7:24 PM: John Beck(Ins): With us, Julius and Meghan?
7:24 PM: Julius Uwansc: yes am here
7:24 PM: John Beck(Ins): Go to page 13, please.
7:24 PM: Meghan Wheeler: yes
7:24 PM: John Beck(Ins): Go to page 14, please.
7:24 PM: Meghan Wheeler: sorry taking notes but I follow
7:25 PM: John Beck(Ins): No problem, Methan.
7:25 PM: John Beck(Ins): Meghan.
7:25 PM: John Beck(Ins): Go to page 15, please.
7:25 PM: John Beck(Ins): I'm big on sketching a graph!
7:25 PM: John Beck(Ins): Go to page 16, please.
7:25 PM: Jennifer Ann Johnson: A = .466
7:25 PM: John Beck(Ins): I'm not ignoring you, Jenn.
7:26 PM: Jennifer Ann Johnson: That's okay
7:26 PM: John Beck(Ins): Notice that I've shaded the region between z = .50 and z = 1.83
7:26 PM: John Beck(Ins): I refer to this as a "detached" region.
7:26 PM: Julius Uwansc: why is that
7:26 PM: John Beck(Ins): A detatched region doesn't touch the line z = 0.
7:27 PM: Julius Uwansc: ok
7:27 PM: John Beck(Ins): Remember, our Table has a shaded region that touches z = 0
7:27 PM: John Beck(Ins): In this case, our shaded region doesn't touch z = 0
7:27 PM: John Beck(Ins): Go to page 17, please.
7:27 PM: John Beck(Ins): Abut (touches).
7:27 PM: John Beck(Ins): Go to page 18, please.
7:28 PM: John Beck(Ins): Here's our algorithm for determining the area that is "detatched."
7:28 PM: John Beck(Ins): Go to page 19, please.
7:28 PM: John Beck(Ins): z = .50 and z = 1.83 were the z values.
7:28 PM: John Beck(Ins): Go to page 20, please.
7:29 PM: John Beck(Ins): Make sense?
7:29 PM: Jennifer Ann Johnson: Yes
7:29 PM: Meghan Wheeler: yes
7:29 PM: John Beck(Ins): DON'T FORGET TO SKETCH A GRAPH.
7:29 PM: Julius Uwansc: yes
7:29 PM: John Beck(Ins): Go to page 21, please.
7:29 PM: John Beck(Ins): For z = 1.83, A = .466
7:29 PM: John Beck(Ins): Go to page 22, please.
7:30 PM: John Beck(Ins): For Z = .50, A = .192
7:30 PM: John Beck(Ins): Go to page 23, please.
7:30 PM: John Beck(Ins): Then we subtract.
7:30 PM: John Beck(Ins): For "Detatched regions" we will always subtract.
7:30 PM: John Beck(Ins): Go to page 24, please.
7:31 PM: John Beck(Ins): Hmmmm. I suspect that w'ere going to get to find out what z stands for -- FINALLY.
7:31 PM: John Beck(Ins): Go to page 25, please.
7:32 PM: John Beck(Ins): For a normal distribution, the mean is at the middle of the curve.
7:32 PM: John Beck(Ins): Since the mean is 7.5, we put 7.5 in the middle of the curve.
7:32 PM: John Beck(Ins): Since 7.3 is smaller than 7.5, we put 7.3 to the left of 7.5. Then we shade our region.
7:33 PM: John Beck(Ins): Go to page 26, please.
7:33 PM: Julius Uwansc: ok
7:33 PM: John Beck(Ins): FINALLY!!!
7:33 PM: John Beck(Ins): the formula for z is: z = (x - xbar)/s
7:34 PM: John Beck(Ins): x - xbar is the "the amount by which x deviates from the mean (xbar)."
7:34 PM: John Beck(Ins): Then we divide by s which is the standard deviation for our sample.
7:35 PM: John Beck(Ins): So z measures the number of standard deviations that x deviates from the mean.
7:35 PM: John Beck(Ins): Okay?
7:35 PM: Jennifer Ann Johnson: yes
7:35 PM: Meghan Wheeler: okay
7:35 PM: John Beck(Ins): Go to page 27, please.
7:35 PM: John Beck(Ins): Notice that z is a negative number.
7:35 PM: Julius Uwansc: yes
7:35 PM: John Beck(Ins): No big deal since the normal curve is Symmetric about the mean.
7:36 PM: John Beck(Ins): Go to page 28, please.
7:36 PM: John Beck(Ins): So 5.2% of the scores lie between 7.3 and 7.5
7:36 PM: John Beck(Ins): Okay?
7:36 PM: Jennifer Ann Johnson: got it
7:36 PM: Meghan Wheeler: got it
7:36 PM: Julius Uwansc: ok
7:36 PM: John Beck(Ins): Go to page 29, please.
7:37 PM: John Beck(Ins): Go to page 30, please.
7:37 PM: John Beck(Ins): Always sketch a graph!
7:37 PM: John Beck(Ins): Go to page 31, please.
7:37 PM: John Beck(Ins): The mean is 10, so 10 is in the middle of the normal curve.
7:37 PM: John Beck(Ins): 12 is greater than 10, so 12 is to the right of 10.
7:38 PM: John Beck(Ins): We want the area that is greater than 12, so we've shaded the region to the right of 12.
7:38 PM: John Beck(Ins): Okay?
7:38 PM: Jennifer Ann Johnson: okay
7:38 PM: Meghan Wheeler: okay
7:38 PM: John Beck(Ins): Go to page 32, please.
7:39 PM: John Beck(Ins): Here's our algorithm. Remember, our shaded region is "detatched" so we're going to have to subtract.
7:39 PM: John Beck(Ins): Go to page 33, please.
7:39 PM: John Beck(Ins): Go to page 34, please.
7:40 PM: John Beck(Ins): Go to page 35, please.
7:40 PM: John Beck(Ins): For a "normal" distribution, 1/2 of the scores are to the right of the middle point.
7:40 PM: John Beck(Ins): Go to page 36, please.
7:41 PM: John Beck(Ins): We have to use or z formula to detrmine the area between x = 10 and x = 12.
7:41 PM: John Beck(Ins): Go to page 37, please.
7:41 PM: John Beck(Ins): Go to page 38, please.
7:41 PM: John Beck(Ins): Okay?
7:41 PM: Jennifer Ann Johnson: yes
7:42 PM: Julius Uwansc: yes
7:42 PM: Meghan Wheeler: yes
7:42 PM: John Beck(Ins): Okay, Class, we have to cover Ch 11 tonight.
7:42 PM: Jennifer Ann Johnson: I'm there
7:42 PM: John Beck(Ins): Let me know when you're on Ch 11 p1, please.
7:43 PM: Meghan Wheeler: there
7:43 PM: Julius Uwansc: am on 11
7:43 PM: John Beck(Ins): Go to page 2, please.
7:43 PM: John Beck(Ins): Always sketch a graph!
7:43 PM: John Beck(Ins): 40% = .40
7:44 PM: John Beck(Ins): And since this is the area, we show this as the amount of the shaded region.
7:44 PM: John Beck(Ins): Go to page 3,please.
7:44 PM: John Beck(Ins): This came directly from our table.
7:44 PM: John Beck(Ins): Go to page 4, please.
7:45 PM: John Beck(Ins): Go to page 5, please.
7:45 PM: Julius Uwansc: I have to go now, my boss is here
7:45 PM: John Beck(Ins): No problem, Julius.
7:45 PM: Julius Uwansc has left the room.
7:45 PM: John Beck(Ins): Go to page 6, please.
7:45 PM: John Beck(Ins): So 40% of the scores lie between z = 0 and z = 1.28
7:45 PM: John Beck(Ins): Okay?
7:45 PM: Meghan Wheeler: got it
7:46 PM: Jennifer Ann Johnson: got it
7:46 PM: John Beck(Ins): Go to page 7, please.
7:46 PM: John Beck(Ins): Don't forget to sketch a graph!
7:46 PM: John Beck(Ins): Go to page 8, please.
7:46 PM: John Beck(Ins): The mean, 55 is in the middle of the normal curve.
7:47 PM: John Beck(Ins): 50% of the scores are below the mean (median, mode).
7:47 PM: John Beck(Ins): And since we are looking for 80% of the scores we have also shaded the region that has 30% of the scores to the right of the mean.
7:47 PM: John Beck(Ins): 50% + 30% = 80%.
7:47 PM: John Beck(Ins): Okay?
7:47 PM: Jennifer Ann Johnson: right
7:47 PM: Meghan Wheeler: yes
7:48 PM: John Beck(Ins): Go to page 9, please.
7:48 PM: John Beck(Ins): Go to page 10, please.
7:48 PM: John Beck(Ins): Now it's a matter of substituting values for z, xbar and s.
7:49 PM: John Beck(Ins): Go to page 11, please.
7:49 PM: John Beck(Ins): We have a 3 in the denominator to the right of the equal sign, so we multiply the expressions on both sides of the equal sign by 3.
7:49 PM: John Beck(Ins): That will remove or denominator, 3.
7:49 PM: John Beck(Ins): Go to page 12, please.
7:50 PM: John Beck(Ins): 3(.084) = 2.52
7:50 PM: Meghan Wheeler: the 3 is the standard deviation?
7:50 PM: John Beck(Ins): Yes, Meghan.
7:50 PM: Meghan Wheeler: okay got it
7:50 PM: John Beck(Ins): Go to page 13, please.
7:51 PM: John Beck(Ins): A little algebra!
7:51 PM: John Beck(Ins): Go to page 14, please.
7:51 PM: John Beck(Ins): So 80% of the scores are below 57.52
7:51 PM: John Beck(Ins): Okay?
7:51 PM: Jennifer Ann Johnson: yes
7:51 PM: Meghan Wheeler: yes
7:51 PM: John Beck(Ins): Go to page 15, please.
7:52 PM: John Beck(Ins): This is a bar graph.
7:52 PM: John Beck(Ins): Notice that the bar is taller at 9
7:52 PM: John Beck(Ins): In fact it is tallest at 9.
7:52 PM: John Beck(Ins): We expect to get more 9s than any other score.
7:52 PM: John Beck(Ins): The bars are shortest at 0 and 18.
7:53 PM: John Beck(Ins): We expect to get very few 0s and 18s
7:53 PM: John Beck(Ins): Not very often will you toss a coin 18 times and get 18 heads.
7:53 PM: John Beck(Ins): Similarly with 0 heads.
7:53 PM: John Beck(Ins): Okay?
7:53 PM: Jennifer Ann Johnson: yes
7:53 PM: Meghan Wheeler: yes
7:54 PM: John Beck(Ins): There are situations when we can use a normal approximation for a binomial experiment.
7:54 PM: John Beck(Ins): So instead of using that C(n,r)p^r(q^(n-r) formula.
7:55 PM: John Beck(Ins): We can use a normal curve to approximate our value.
7:55 PM: John Beck(Ins): Let's click on Tools, the Definitions, please.
7:56 PM: John Beck(Ins): So, to use a normal approximation, we need to test n times p and n times q
7:56 PM: John Beck(Ins): If both of these products are greater than 5, then we can use a "normal approximation."
7:57 PM: John Beck(Ins): And we can determine the mean by multiplying n by p\
7:57 PM: John Beck(Ins): And we can determine the standard deviation, s, by determining the square root of n times p times q.
7:57 PM: John Beck(Ins): Sounds like fun to me!
7:57 PM: John Beck(Ins): Okay?
7:57 PM: Jennifer Ann Johnson: too much fun
7:57 PM: John Beck(Ins): lol
7:58 PM: John Beck(Ins): Okay, let's click on "Hide 'em" please.
7:58 PM: Meghan Wheeler: getting it
7:58 PM: John Beck(Ins): Go to page 16, please.
7:58 PM: John Beck(Ins): Go to page 17, please.
7:58 PM: John Beck(Ins): WE are looking for the probablity that we get at least 11 heads.
7:59 PM: John Beck(Ins): Notice that I've shaded the region that is greater than 10.5 heads.
7:59 PM: Jennifer Ann Johnson: that would be 11-18, correct?
7:59 PM: John Beck(Ins): That's because 10.5, 10.6, 10.7, 10.8, 10.9 would be rounded off to 11 heads.
7:59 PM: John Beck(Ins): RIGHT, Jenn.
8:00 PM: John Beck(Ins): Go to page 18, please.
8:00 PM: John Beck(Ins): We are looking for the area of a "detatched" region, so we'll need to subtact!
8:00 PM: John Beck(Ins): Go to page 19, please.
8:00 PM: John Beck(Ins): Go to page 20, please.
8:01 PM: John Beck(Ins): First of all, we need to determine xbar.
8:01 PM: John Beck(Ins): The mean is 9.
8:01 PM: John Beck(Ins): Go to page 21, please.
8:02 PM: John Beck(Ins): I've rounded off to 2-decimal places. Unless istructed otherwise, round off to 2-decimal places.
8:02 PM: John Beck(Ins): Go to page 22, please.
8:02 PM: John Beck(Ins): Go to page 23, please.
8:02 PM: John Beck(Ins): Go to page 24, please.
8:03 PM: John Beck(Ins): For z = .71, A = .261
8:03 PM: John Beck(Ins): Go to page 25, please.
8:03 PM: John Beck(Ins): Remember, I told you we'd need to subtract.
8:03 PM: John Beck(Ins): Go to page 26, please.
8:03 PM: John Beck(Ins): The probability of this detatched region is .239
8:03 PM: John Beck(Ins): Okay?
8:04 PM: Jennifer Ann Johnson: yes
8:04 PM: Meghan Wheeler: yes
8:04 PM: John Beck(Ins): One more problem, Class, then you get to have supper.
8:04 PM: John Beck(Ins): Go to page 27, please.
8:04 PM: John Beck(Ins): Exactly 8 heads would be between 7.5 heads and 8.5 heads.
8:04 PM: John Beck(Ins): Okay?
8:05 PM: Jennifer Ann Johnson: yes
8:05 PM: Meghan Wheeler: okay
8:05 PM: John Beck(Ins): Go to page 28, please.
8:05 PM: John Beck(Ins): We've already calculated xbar and s.
8:05 PM: John Beck(Ins): Go to page 29, please.
8:06 PM: John Beck(Ins): First we need to calculate the area between x = 9 and x = 7.5
8:06 PM: John Beck(Ins): Go to page 30, please.
8:06 PM: John Beck(Ins): Then we need to calculate the area between x = 8.5 and x = 9
8:06 PM: John Beck(Ins): Go to page 31, please.
8:07 PM: John Beck(Ins): I warned you that we'd have to subtract -- notice we have a detatched region.
8:07 PM: John Beck(Ins): Okay, Jenn and Meghan?
8:07 PM: Jennifer Ann Johnson: yes sir
8:07 PM: Meghan Wheeler: still working it out but getting there
8:08 PM: John Beck(Ins): I haven't received your tests yet, but I should be posting grades for Test 2 by Saturday of this week.
8:08 PM: John Beck(Ins): Have a good one, Class.
8:08 PM: Jennifer Ann Johnson: Thanks, you too
8:08 PM: John Beck(Ins): By the way, you're almost ready for Test 3!!!!!
8:08 PM: Meghan Wheeler: thank you ...you too!
8:08 PM: Jennifer Ann Johnson: Can't wait
8:08 PM: John Beck(Ins): lol
8:08 PM: John Beck(Ins): G'night!
8:08 PM: Jennifer Ann Johnson: good night
8:08 PM: Jennifer Ann Johnson has left the room.
8:09 PM: John Beck(Ins) has left the room.
8:09 PM: Meghan Wheeler has left the room.