Over 50 of family households in the us have no chil dren...

Over 50% of family households in the U.S. have no children under 18 living at home and fewer than 10% have 3 or more, so the distribution of the number of children living in family households is skewed to the right. The mean is 0.96 children, with a standard deviation of 1.26 children. What's the probability that in a random sample of 250 family households the mean number of children living in those homes will be greater than 1? A) 0.056 B) 0.308 C) 0.487 D) It cannot be determined because the sample is not large enough. E) It cannot be determined because the population distribution is not normal.

Transcript

00:01 In this problem, they tell us that the amount of children that us household have has a mean of 0 .96 and a standard of vision of 1 .196.

00:12 Now, they kind of warn us that the, they kind of warn us that this distribution is a little skewed, so it's skewed right.

00:23 However, they tell us that they're going to take a sample of 250 houses and they want to do.

00:30 Know what the probability is that they will have more than one children, greater than one children.

00:37 Because even though the population is not normally used to it, it is skewed, when we take a sample, if the sample is bigger than 30, the central limit theorem tells us that we can't, that sample, that is going to have produce a sampling distribution, and the sampling distribution is normally distributed.

00:57 And it's going to have the mean, the same mean as the population and it's going to have a standard deviation but of the sampling distribution which is s is going to have a standard error of this the standard deviation of the population divided by the square root of n where n is the sample size which is in this case 250 so the sample is substantial so this will be 1 .26 divided by the square root of so it's going to be really small.

01:36 That gives a value of 0 .0769.

01:42 So now that we know that, well, we can compute the probability that they want.

01:46 They want to know what the probability did that's going to have be one or more.

01:50 One is going to be a little bit above.

01:53 A little bit here so we can see it a little bit above.

01:57 Here's going to be one.

01:58 And we want to know this area...

Question

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