00:01
Okay, so we have a study that tells us that a television fan watches a mean of 10 hours per week with a standard deviation of 2 .2 hours, and it's approximately normally distributed.
00:14
So first, we are asked, what's the probability that a randomly selected sport fan watches more than 12 hours per week? so to find that, we're just going to find the z score, which is x minus mu over sigma.
00:32
So this is the probability that x is greater than 12, right? so x is going to be our 12 minus our mean of 10 over a standard deviation.
00:41
This will tell us how many serenid deviations above the mean this is.
00:44
So 2 divided by 2 .2 is 0 .91.
00:55
Okay.
00:56
And when i look up the probability of being greater than that on my.
01:02
Chart right so i'm looking up 0 .91 on the chart and when i look that up it gives me 0 .816 but that's the probability that it's less than 0 .91 or yeah that z is less than 0 .91 i need the probability that it's greater so i need to take 1 minus the probability which gives me 0 .1814 so that's for part a for part b for part b we're told that if we're asked if 5 ,000 sports fans are surveyed, um how many would have watched for more than 12 hours, right? so all we need to do here is take that 5 ,000 and multiply by the probability that we just found, the probability of, um, one person.
02:00
So when we take this probability, 0 .1814, and we multiply that by 5 ,000, we get 907.
02:15
So that would be our estimated number who actually watched more than that much.
02:20
For c, we're asked what percentage of sports fans watch sports for less than one hour per week.
02:28
So we're going to once again find a z score.
02:31
It's going to be our x minus our mu over our standard deviation.
02:38
So that's going to be negative 9.
02:42
Over 2 .2 which is negative 4 .09 and when you look up that value on your z table it is minuscule, just so tiny that um like four standard deviations below the mean is like way way way way way over there.
03:02
So when you look up that probability that probability is less than 0 .001.
03:09
Okay so um so that's the answer to that is like less like almost 0.
03:19
For d, we are asked one in three sports fans spend more than how many hours watching sports.
03:26
So one in three is the same as one -third, which is .33 approximately.
03:31
So if we're looking at our distribution here, 0 .33, we're asked to find like 33 spend more than how many hours.
03:44
So we're looking for the area that makes this equal to 0 .33 right here.
03:49
So i need to find the z score that makes that happen.
03:53
So basically i just have to go backwards from my z table for this.
04:00
And when i do that, i get 0 .44 for the z score that makes that happen...