# Tutor.com Probabilities Session

##### Sep. 30, 2012

Session Transcript - Math - Statistics, 8/22/2012 8:05PM - Tutor.comSession Date: 8/22/2012 8:05PM
Length: 105.7 minute(s)
Subject: Math - Statistics

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[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Monica (Customer)
[00:00:00] Im unsure of what to do with this homework assignment [ File > http://lhh.tutor.com/SharedSessionFiles/35b803d2-523a-4cd3-9a5f-9edc1573c4ca_binomial_dist_ps.docx ]

Patrick S (Tutor)
[00:00:23] Welcome to Tutor.com !

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Monica (Customer)
[00:01:07] hello

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Patrick S (Tutor)
[00:01:16] Hi!

Monica (Customer)
[00:01:54] ok ty im going to run to rest room

Patrick S (Tutor)
[00:02:02] ok
[00:03:53] Ok. I'm ready to start when you are.

Monica (Customer)
[00:06:35] k
[00:06:50] sorry my 4 yr old needed help

Patrick S (Tutor)
[00:06:58] ok. .. no problem
[00:07:17] What do you think about part a. ?

Monica (Customer)
[00:07:59] not sure this is really confusing for me having a very hard time with this course

Patrick S (Tutor)
[00:08:25] Let's say that are 100 people in Hialgo County.
[00:08:43] How many would be Mexican-American?

Monica (Customer)
[00:09:29] 50

Patrick S (Tutor)
[00:10:01] what percent would that be?

Monica (Customer)
[00:10:32] 50

Patrick S (Tutor)
[00:11:02] is that the percent of Hidalgo County that is Mexican-America?

Monica (Customer)
[00:11:50] no 79.1

Patrick S (Tutor)
[00:11:55] corect
[00:12:47] So, if we only have 100 people how many of those would be Mexican-Amercan?

Monica (Customer)
[00:13:13] so would that be the probality 79.1%

Patrick S (Tutor)
[00:14:05] probabilities are always between 0 and 1 inclusive . . .So, convert 79.1% to a decimal

Monica (Customer)
[00:14:26] 0.791

Patrick S (Tutor)
[00:14:37] exactly!
[00:15:04] Now, part b

Monica (Customer)
[00:16:33] yes
[00:16:59] so would I minus 100 - 79.1 = 20.9?
[00:17:29] and how do I briefly explain

Patrick S (Tutor)
[00:17:35] close . . .remember what we said about probabilities (how big they are)

Monica (Customer)
[00:18:14] ???? confused

Patrick S (Tutor)
[00:18:54] 20.9 is too big because a probability is always between 0 and 1 inclusive

Monica (Customer)
[00:19:08] .209

Patrick S (Tutor)
[00:19:12] there you go!
[00:19:41] So, now why does that work?

Monica (Customer)
[00:19:56] because it is between 0 and 1?

Patrick S (Tutor)
[00:21:04] ok . . right . . sorry what I meant was why is the probability that a juror will not be Mexican-American .209 ?

Monica (Customer)
[00:22:10] because it is 20.9 and move the decimal point 2 places

Patrick S (Tutor)
[00:23:01] ok, but i'm trying to go back to the question you asked earlier:
[00:23:13] so would I minus 100 - 79.1 = 20.9?
[00:17:29] and how do I briefly explain

Monica (Customer)
[00:24:32] Oh ok im still unsure I just used that equasion, and moved the decimal point

Patrick S (Tutor)
[00:25:13] Right . . I think they want you to talk about the equation in your explanation.

Monica (Customer)
[00:25:31] oh ok then
[00:25:42] basically showing my work'

Patrick S (Tutor)
[00:26:30] you might also want to state briefly why you subtracted from 100

Monica (Customer)
[00:27:53] because it is the whole and when u subtract 79.1 the 20.9 is left from the whole I understand how to explain it now to part c

Patrick S (Tutor)
[00:28:11] Great!
[00:28:41] do you know what n and p represent?

Monica (Customer)
[00:29:24] not really guessin n=79.1%
[00:29:32] p=7

Patrick S (Tutor)
[00:30:03] sorry, that's not correct . . It's usually best not to guess
[00:30:37] This is a binomial problem

Monica (Customer)
[00:30:47] ok

Patrick S (Tutor)
[00:30:53] In a binomial problem n an p have specific meanings
[00:31:27] n is the number of trials or the number of times we do a random selection
[00:31:54] So, how many random selections do we need to fill the jury?

Monica (Customer)
[00:32:05] 12

Patrick S (Tutor)
[00:32:08] yes!
[00:32:43] p is the probability of success when we do a random selection

Monica (Customer)
[00:32:54] 79.1

Patrick S (Tutor)
[00:33:03] is that a probability?

Monica (Customer)
[00:33:11] 0.791

Patrick S (Tutor)
[00:33:15] That's it!

Monica (Customer)
[00:33:44] x=7

Patrick S (Tutor)
[00:34:21] well don't know the specific value of x yet. It could be 7
[00:34:30] It also could be 1

Monica (Customer)
[00:34:33] oh ok

Patrick S (Tutor)
[00:34:54] in fact it could be anything from 1 to 12

Monica (Customer)
[00:35:14] because n- 12
[00:35:19] n=12

Patrick S (Tutor)
[00:35:22] right
[00:35:28] Ok. any questions about part c?

Monica (Customer)
[00:35:34] no

Patrick S (Tutor)
[00:36:19] oops on that last one I left out 0
[00:36:32] we could have 0 Mexican-Americans

Monica (Customer)
[00:36:50] oh ok

Patrick S (Tutor)
[00:37:03] Now part
[00:37:05] d

Monica (Customer)
[00:37:52] ok

Patrick S (Tutor)
[00:38:33] We need to find the probability that 7 or fewer will be Mexican-Americans
[00:39:06] Are you allowed to use a table or calculator to find the binomial?

Monica (Customer)
[00:39:14] yes

Patrick S (Tutor)
[00:39:21] Great!
[00:39:37] So, we already know n and p
[00:39:58] What else to we need?

Monica (Customer)
[00:40:05] q

Patrick S (Tutor)
[00:40:17] good and what is q?

Monica (Customer)
[00:40:48] 7
[00:41:09] no n*p

Patrick S (Tutor)
[00:41:28] no, not 7. Hint: we've already done it we just didn't call it p

Monica (Customer)
[00:41:40] 0.791

Patrick S (Tutor)
[00:41:44] that's p

Monica (Customer)
[00:41:52] .209

Patrick S (Tutor)
[00:41:58] that's it
[00:42:20] q is the probability of failure
[00:42:32] since the prob. of success is .791
[00:42:39] the prob. of failure has to be .209

Monica (Customer)
[00:42:55] ok

Patrick S (Tutor)
[00:42:59] Now we can you a binomial chart or calculator
[00:43:13] do you know how to do that part?

Monica (Customer)
[00:43:30] z table

Patrick S (Tutor)
[00:43:58] no, not a z-table . . a binomial table, or the binomial function in your calculator

Monica (Customer)
[00:44:23] ok i have the table

Patrick S (Tutor)
[00:44:27] goo
[00:44:29] d
[00:44:32] good

Monica (Customer)
[00:45:11] just dunnot what to look for

Patrick S (Tutor)
[00:45:45] can you share your table . . textbooks tend to set them up differently

Monica (Customer)
[00:46:14] cannot because im look at it in my book

Patrick S (Tutor)
[00:47:12] do you have a camera phone? take a picture of the page and up load it? (make sure there's no personal info in the picture)

Monica (Customer)
[00:48:23] ok give me a min

Patrick S (Tutor)
[00:48:29] k
[00:50:42] I'm working on this...
[00:52:42] I'm working on this...

Monica (Customer)
[00:53:12] File Shared > img_20120822_205623.jpg

[00:53:34] File Shared > img_20120822_205630.jpg
[00:53:48] this is the best I could do

Patrick S (Tutor)
[00:55:08] ok . . so what's the first column?

Monica (Customer)
[00:55:22] n = 12

Patrick S (Tutor)
[00:55:44] n . . right so we need to find the row that starts with 112
[00:55:47] oops 1
[00:55:48] 2
[00:55:48] 12
[00:55:51] ha

Monica (Customer)
[00:56:05] huh?

Patrick S (Tutor)
[00:56:24] the first column is the number of trails, n

Monica (Customer)
[00:56:37] ok im at 12

Patrick S (Tutor)
[00:56:43] good!
[00:57:02] the second column is the number of successes
[00:57:16] we want 7 or fewer

Monica (Customer)
[00:57:30] ok

Patrick S (Tutor)
[00:57:48] now the rest of the columns are values of p
[00:58:04] find the one closest to .791
[00:59:54] did you find it?

Monica (Customer)
[01:00:02] no
[01:00:48] .70

Patrick S (Tutor)
[01:00:49] we're looking at the top of the chart . . . see the values that start with .01 .05 .15 .20 etc?
[01:01:06] ok what's closer to 79.1, .70 or .80?

Monica (Customer)
[01:01:15] .80

Patrick S (Tutor)
[01:01:18] right

Monica (Customer)
[01:01:33] .053

Patrick S (Tutor)
[01:01:39] excellent!
[01:02:05] This tells us the probability of picking 7 Mexican-Americas for the jury is .053
[01:02:21] Now we want 7 or fewer

Monica (Customer)
[01:03:19] .016, .003, .001, rest are 0's

Patrick S (Tutor)
[01:03:31] good
[01:03:41] now we add these probabilities up

Monica (Customer)
[01:04:06] .55

Patrick S (Tutor)
[01:04:10] right!
[01:04:38] so the probability of of getting 7 or fewer Mexican-Americans is .55 . . .a little more than 50% !
[01:06:14] We could also say, if we picked 100 different juries, we would expect 55 of them to have 7 or fewer Mexican-Americans

Monica (Customer)
[01:07:30] ok make somewhat sence

Patrick S (Tutor)
[01:07:48] great! I'm glad to hear it.

Monica (Customer)
[01:08:08] no wpart e

Patrick S (Tutor)
[01:08:14] right
[01:08:25] I think there's a typo in that problem
[01:08:42] should be referring back to part d not part c

Monica (Customer)
[01:09:06] yes i see that
[01:10:03] I woukd agree because it is more than half that are of the same race that has been selected
[01:10:17] for his trial

Patrick S (Tutor)
[01:10:43] true . . .but in the whole county 79.1% are his race

Monica (Customer)
[01:11:11] so it os almost 3/4 of his peers than
[01:11:40] is more than 3/4 of his peers
[01:11:48] 79.1%

Patrick S (Tutor)
[01:12:09] well . . we want 79.1% of the jury to be Mexican-American
[01:12:34] and there's 12 total on the jury . . so how many

Monica (Customer)
[01:12:50] 7

Patrick S (Tutor)
[01:13:20] we need to know what x is

Monica (Customer)
[01:13:35] .209

Patrick S (Tutor)
[01:14:00] isn't that 1 - .791 ?

Monica (Customer)
[01:14:39] yes sorry told u it is confusing but it would be 0.209

Patrick S (Tutor)
[01:15:06] is that the same as .791 = x / 12 ?

Monica (Customer)
[01:15:52] no

Patrick S (Tutor)
[01:15:56] good
[01:16:28] we need to find the number of Mexican-Americans that will make the proportion come out to .791
[01:16:51] Can you solve that equation?

Monica (Customer)
[01:17:47] no sure
[01:17:52] im sorry

Patrick S (Tutor)
[01:18:06] it's OK . . .multiply both sides by 12

Monica (Customer)
[01:19:11] 9.492 = x

Patrick S (Tutor)
[01:19:16] right!
[01:19:39] ah ha! now I see why thy refer back to part c, and not part d

Monica (Customer)
[01:20:40] at that point it is less than 10% of his peers

Patrick S (Tutor)
[01:21:08] remember x is the number of mexican-americans
[01:21:19] so, it's actually 9 are his race

Monica (Customer)
[01:22:02] and 9 out of 12 is like the majority of his peers

Patrick S (Tutor)
[01:22:17] yes. . . just like it is in the whole county
[01:22:52] it's 79.1% in the county . . the Judge is arguing that it should be 79.1% in the jury also
[01:23:54] Now we need to know if this is a reasonable requirement
[01:24:18] In other words, what's the probability we can get 9 Mexican-Americans on the jury

Monica (Customer)
[01:24:39] 79.1%

Patrick S (Tutor)
[01:25:24] that's the proportion of jurors who are Mexican-American

Monica (Customer)
[01:25:39] 7
[01:25:51] 7 out of 12

Patrick S (Tutor)
[01:25:53] we need to use the binomial table to find x=7
[01:26:27] oops x=9
[01:26:28] sorry

Monica (Customer)
[01:26:50] in where n = 0.236

Patrick S (Tutor)
[01:27:00] n is still 12
[01:27:08] x=9

Monica (Customer)
[01:27:21] n = 12

Patrick S (Tutor)
[01:27:25] yes

Monica (Customer)
[01:27:41] 0.236

Patrick S (Tutor)
[01:27:59] goo
[01:28:03] good!
[01:28:42] so, the probability of getting 9 Mexican-Americans on the jury is .236

Monica (Customer)

Patrick S (Tutor)
[01:30:30] correct . . so if we seat 100 different juries, we'd expect about 24 of them to be 79.1% mexican-american
[01:30:49] so, is the Judge's decision resonable?

Monica (Customer)
[01:31:24] yes because it is a quarted of the the population

Patrick S (Tutor)
[01:34:29] the 24% is referring to possible juries, not the population

Monica (Customer)
[01:35:11] oh ok

Patrick S (Tutor)
[01:35:16] Look at this way . .what percent of juries would not have 9 mexican-americas?

Monica (Customer)
[01:35:32] 76%

Patrick S (Tutor)
[01:35:35] right
[01:36:18] what's more likely seating a jury with exactly 9 or a jury that doesn't have exactly 9?

Monica (Customer)
[01:36:47] exactly 9

Patrick S (Tutor)
[01:37:02] but that only happens 24 times out of 100
[01:37:40] isn't it more likely we'll get a jury with less than 9 or maybe greater than 9?

Monica (Customer)
[01:38:59] less than 9

Patrick S (Tutor)
[01:39:36] we'd say not 9 (could be more or less, just not exactly 9)
[01:40:12] so, then is it reasonable for the Judge to reject his trail because he had only 7 on his jury?

Monica (Customer)
[01:40:38] ok it make more sence now ty

Patrick S (Tutor)
[01:40:46] great!
[01:40:54] Do you have any questions about anything we went over today?

Monica (Customer)
[01:41:25] no not now but may with other homeworks I have but ty for now

Patrick S (Tutor)
[01:41:42] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â
[01:44:43] I'm working on this...