A survey collected data about the number of TVs that a...

A survey collected data about the number of TVs that a family of four has in their household. The number of TVs is distributed as shown. Find the mean, variance, and standard deviation for the distribution. (Write answers rounded to one decimal place. Use the letter A or B to answer the question about units.) # of TVs (x) P(x) 0 0.05 1 0.15 2 0.45 3 0.30 4 0.05 The mean is Are the mean's units A: TVs or B: $TVs^2$? The variance is Are the variance's units A: TVs or B: $TVs^2$? The standard deviation is Are the standard deviation's units A: TVs or B: $TVs^2$?

Transcript

00:01 This probability table and we're going to be answering some questions about it.

00:05 So what percentage of houses have at least one tv? so to do this, we're going to go to the number of tv, go to one.

00:15 Then because it says at least, we'll take all the ones greater than it.

00:21 And we're going to add up all of these probabilities.

00:24 So 31 .4 plus 23 plus 23 plus 20.

00:31 Point four plus 13 plus 6 .3 and when you add all of that up you get 98 .1 percent.

00:43 So what percentage of households have at most free? so at most free means we go to free and take all the ones that are lower than it.

00:53 So we're going to have 1 .9 plus 31 .4 plus 23 plus 24.

01:02 And that gives us 80 .7%.

01:08 What percentages of households have three or more? so we go to free and add it to the ones that are greater than it.

01:23 So 24 .4 plus 13 plus 6 .3 and that gives us 43 .7%.

01:34 So is this a binomial probability? experiment.

01:41 So if you so is there only two outcomes either you have a tv or you don't have a tv? well no actually because this is asking how many tvs do you have.

01:57 So there is more than two outcomes.

02:01 So this is actually not binomial.

02:04 Is it a probability distribution? well to check this, we're going to add up all the probabilities, and if it equals 100, then it is a probability distribution.

02:17 Now, in part a, we added up all of them except the 1 .9 at the beginning.

02:23 So is 98 .1 plus 1 .9 equal to 100? well, that's a yes.

02:30 So this is a probability distribution because the sum of all of the percentages add up to 100.

02:40 Now finally, we're going to find the mean and standard deviation.

02:45 And because we're just given this table, we sadly have to do this the long way.

02:52 So the fine mean, we're going to take each x, multiply it by its probability, and then add all of them up.

03:01 So what that means, mean is equal to the first one is zero times 1 .9...

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