00:01
Alright, so for the question about vegetarian college students, suppose that 8 % of college students are vegetarian.
00:06
Part a, the distribution of sample proportion of vegetarians in random samples of size 60 is approximately normal since n is greater than 30.
00:17
This would be true because of the central limit theorem, clt, central limit theorem, which states that as long as n is greater than 30, the distribution of sample proportions will be approximately normal.
00:32
And since 60 is greater than 30, that one would be approximately normal.
00:41
For b, this would be false, also using the central limit theorem.
00:46
Since b is talking about it being right skewed with a sample size of 50, 50 once again is greater than 30.
00:53
So, as long as the population proportion is about 8%, then yes, this would also be normally skewed.
01:01
So, it would not be right skewed, so b would be false.
01:04
Going on to c, c where a random sample of 125 college students and 12 % are vegetarian would be unusual.
01:14
You'd start by using the standard deviation formula, which is pq over n, p being your percent, q being q is equal to 1 minus p.
01:24
So, it would be 0 .08 % times 0 .92 % over 125, which would come out to about 0 .024.
01:39
And usually for something to be unusual like that, it's at least two standard deviations away.
01:44
So, you take this times two, you get 0 .048...
