Tutor.com Probabilities Session

Mar. 15, 2012

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Session Transcript - Math - Statistics, 3/12/2012 8:02PM - Tutor.comSession Date: 3/12/2012 8:02PM
Length: 37.8 minute(s)
Subject: Math - Statistics


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

Guest (Customer)
[00:00:00] television viewing reached a new high when the Nielsin company reported a mean daily viewing online time of 8.35 hrs per household. Use a normal distribution w/ a standard deviation of 2.5 hrs a.what is the probability that a household views television between 5 and 10 hrs a day/ b. how many hours of television viewing must a household have in order to be in the top 3% of all television viewing households? c. what is the probability that a household views television more than 3 hours a day

Brian H (Tutor)
[00:00:05] Welcome to Tutor.com ! My name is Brian. How are you today?

Guest (Customer)
[00:00:23] pretty good, how about yourself?

Brian H (Tutor)
[00:00:42] i'm very good thanks!
[00:01:13] Have you worked with normal distribution problems like this before?

Guest (Customer)
[00:01:37] a little, i'v just learned the concept

Brian H (Tutor)
[00:02:02] ok good! so for part a) we need to use the formula z = x - mean/ std. dev
[00:02:10] and we're going to have to use a z table

Guest (Customer)
[00:02:16] ok i thought so

Brian H (Tutor)
[00:02:42] and so we're going to have to calculate this twice. one with x = 10 and one with x = 5
[00:02:47] to find the probability between 5 and 10

Guest (Customer)
[00:02:54] ooh okay gotcha

Brian H (Tutor)
[00:03:47] does this make sense so far ?

Guest (Customer)
[00:04:10] yea it equals .66 than i woudl find that on my z graph?
[00:04:15] table

Brian H (Tutor)
[00:04:20] exactly!

Guest (Customer)
[00:04:44] oh ok

Brian H (Tutor)
[00:05:08] and now we calculate the z for when x =5 the same way

Guest (Customer)
[00:06:30] ok got it so would the answer to z after i look it up in the table still be a negative?
[00:06:50] blus i got .0901

Brian H (Tutor)
[00:07:22] right! so no it's no longer negative
[00:07:34] what'd you get for that first probability
[00:07:36] when z = .66

Guest (Customer)
[00:07:54] i got .7454

Brian H (Tutor)
[00:08:13] good! so that's the probability that the amount of hours is 10 or below
[00:08:21] and -1.34 is 5 or below
[00:08:33] so we need to subtract that to find the probability in between 5 and 10
[00:08:35] does that make sense?

Guest (Customer)
[00:09:49] when it comes to drawing the graph it confuses me a bit

Brian H (Tutor)
[00:09:53] so on the normal graph, .0901 is from that point and everything to the left, and .7454 is everything to the left of that point
[00:10:26] so .0901 means that 9.01% of the time it's less than 5 hours per day of television watched
[00:10:37] but then 74.54% watch 10 hours OR LESS
[00:11:05] but we just want to find the shaded area between 5 and 10
[00:11:15] so we need to subtract .7454-.0901
[00:11:26] because that would be the probability of greater than 5 hours, but less than 10
[00:11:49] keep in mind that .5 is the center of the normal curve
[00:12:01] because 50% of the time it's greater than the mean, 50% less than
[00:12:24] and i also included the corresponding hours values. so 8.35 is the mean and then the 5 and 10 as well
[00:12:47] i know i threw a lot of information at you! Please let me know if that made no sense, or if you have any questions

Guest (Customer)
[00:13:50] okay im a bit confused, on why you shaded the red part, i thought it was jus between 5 and 10

Brian H (Tutor)
[00:14:23] right sorry. so the red is just what the .0901 is. That red is the .0901 of people that watch less than 5 hours
[00:14:38] so all we want is between the 2

Guest (Customer)
[00:15:07] ooh okay, and we would find the propabilty by subtracting the two?

Brian H (Tutor)
[00:15:17] exactly!

Guest (Customer)
[00:16:20] okay so in the books it gives me .6553 but im not getting that

Brian H (Tutor)
[00:16:42] hm.. that should be right! what'd you get when you subtracted .7454- .0901?
[00:16:53] make sure those are the two you're subtracting

Guest (Customer)
[00:16:55] nvm i got it!

Brian H (Tutor)
[00:16:57] k
[00:17:18] you ready for part b) ?

Guest (Customer)
[00:17:26] yes

Brian H (Tutor)
[00:17:41] ok! so then this we're going to solve backwards from the first part

Guest (Customer)
[00:17:55] ok

Brian H (Tutor)
[00:17:58] here it's asking for the amount of hours to be in the top 3%
[00:18:12] so remember the .0901 and .7454 are percentages/probabilities

Guest (Customer)
[00:18:23] so when its asking for percents do we always start backwards?

Brian H (Tutor)
[00:18:40] right! it means we always start with the z table and work backwards
[00:18:52] so it says top 3%, which means .97 or above

Guest (Customer)
[00:19:12] right

Brian H (Tutor)
[00:19:20] so we just want to look up the closest number we can find inside the z table to .9700

Guest (Customer)
[00:19:34] and can you draw the graph please
[00:20:23] and is it 1.82?

Brian H (Tutor)
[00:20:46] very close..
[00:20:48] what
[00:21:00] what's the probability when z = 1.82 though?
[00:21:08] i see .9656
[00:21:30] I believe 1.88 should be .9699, do you see that?

Guest (Customer)
[00:22:13] yea

Brian H (Tutor)
[00:22:29] ok! does that make sense? bc that's the closest probability to .97, so we use 1.88 for our z

Guest (Customer)
[00:23:07] why cant we use 1.89?

Brian H (Tutor)
[00:23:35] we could, it's just a little bit further from .97 than 1.88 is, that's the only reason i chose that. either one is ok though

Guest (Customer)
[00:23:52] ooh okay!

Brian H (Tutor)
[00:24:01] i guess maybe you're right. let's use 1.89 bc it says it wants to be at least in the top 3%
[00:24:07] so 1.88 would be just under that
[00:24:19] and so now we have our z, just not the amount of hours, the X
[00:24:22] so we solve for x
[00:24:50] using this same formula
[00:25:08] so we just multiply both sides by 2.5
[00:25:14] and then add 8.35 to both sides
[00:25:30] and get x = 13.075
[00:25:44] so a household must have at least 13.075 hours to be in the top 3% of viewing!
[00:26:09] any questions about part b) ?

Guest (Customer)
[00:26:44] nope got the same answer

Brian H (Tutor)
[00:27:06] excellent
[00:27:13] and then for c we start it the same way as part a)
[00:27:36] find the z value
[00:27:49] and then look up the corresponding probability inside the z table

Guest (Customer)
[00:28:15] so i got -2.14
[00:29:37] just one question, why are you putting .5 in the middle, you cant put the mean which is 8.35?

Brian H (Tutor)
[00:30:20] we could. but i'm just trying to stay consistent. i've been writing down the probabilities for each z value
[00:30:35] if i was graphing the hours i could do that too. i'd just have 8.35 in the middle. then 3 over to the left
[00:31:19] either one would work : ) we just need to solve for the probability though

Guest (Customer)
[00:31:33] ok gotcha

Brian H (Tutor)
[00:31:34] i got .0162
[00:31:42] and this means 1.62% watch less than 3 hours

Guest (Customer)
[00:31:49] me too

Brian H (Tutor)
[00:31:50] but remember, we want MORE than
[00:31:56] so any ideas how we solve for that?

Guest (Customer)
[00:32:24] not exactly

Brian H (Tutor)
[00:32:56] well remember .5 is the middle underneath the curve. because .5 is to the left and .5 to the right
[00:33:05] which means the total under the normal curve is 1
[00:33:13] so if that little red shaded area is .0162
[00:33:19] then the other part is just 1 - .0162
[00:33:25] so we just do that subtraction

Guest (Customer)
[00:33:45] ooh so the compliment

Brian H (Tutor)
[00:33:51] correct!

Guest (Customer)
[00:34:30] can you shade whivh part is .9828 please

Brian H (Tutor)
[00:35:14] everything all the way to infinity hours up to the right
[00:35:21] or i guess all the way up to 24 hours

Guest (Customer)
[00:35:50] okay got it!wow you were great help!

Brian H (Tutor)
[00:35:59] thanks! did you have any other last questions?

Guest (Customer)
[00:36:25] nope i think i got it!

Brian H (Tutor)
[00:36:30] awesome! great work. have a great night

Guest (Customer)
[00:36:44] thanks!you too!

Brian H (Tutor)
[00:36:51] thanks! bye!