00:01
So there are three different questions here.
00:03
The first one, we have a recent poll finding that 60 % of adults believe that the overall state of moral values is poor.
00:15
So for part a, we are going to randomly select 400 adults, and we want to compute the mean and the standard deviation.
00:29
So this whole problem is dealing with binomial probability.
00:41
And i knew it was dealing with binomial probability because, one, we were working with discrete data.
00:51
There were a fixed number of outcomes, or a fixed number of trials, i should say.
01:03
The trials are independent, and there are only two possible outcomes.
01:21
And we define those outcomes as either success or failure.
01:31
So in this case, our fixed number of trials is the fourth.
01:35
Hundred, the possible outcomes, there's only two of them, either yes, they believed the overall state of moral values is poor, were no, they did not.
01:52
And since it is binomial, we could find the mean by using the formula n times p, we can find the standard deviation by using the formula the square root of n times p times one minus p and we can find probability of x successes by using the formula the combination of n items taken x at a time multiplied by p to the x power multiplied by one minus p to the n minus x power and in all these cases n represents the number of trials.
02:45
P represents your probability of success and x is the number of successes.
03:04
So for part a, we wanted to find our mean, so we'll take n times p.
03:10
There were 400 randomly selected adults, and the probability that they would say, yes, the overall state of moral values is poor, would be 0 .60.
03:23
So that means we have, a mean of 240 and our standard deviation would be found by doing the square root of n times p times the quantity of 1 minus p so that would be the square root of 400 times 0 .60 times the quantity of 1 minus 0 .60 which yields a square root of 90 of 90 which is approximately equal to 9 .7979 -589 -71.
04:09
And it did say to round to only one decimal place, so we would say it was approximately 9 .8.
04:18
For part b, we want to interpret the mean, and our answer choices are, a, for every 400 adults, the mean is the minimum number of them that would be expected to believe the overall state of moral values is poor.
04:50
B, for every 240 adults, the mean is the maximum number of them that would be expected to believe that the overall state of the moral values is poor.
05:02
C, for every 400 adults, the mean is the number of them that would be expected to believe that the overall state of the moral values is poor.
05:09
State of moral values is poor.
05:11
Or d, for every 400 adults, the mean is the range that would be expected to believe the overall state of moral values is poor.
05:21
And your answer is going to be c.
05:25
And then for part c, we want to calculate a probability and decide if it is unusual.
05:39
So for part c, we want to determine would it be unusual if 253 out of the 400 adults believe the overall state is poor? so what we want to do here is we want to calculate the probability that there are 253 successes.
06:27
So we'll use our formula ncx times p to the x times 1 minus p to the n minus x, which would be 400c253 times .60 to the 2503 power times 1 minus .60 to the 253 power.
06:50
To the 400 minus 253 power.
06:56
And in doing so, we are going to get a probability of .01699 -667 to 4.
07:06
And therefore we would say 253 out of 400 believing that the overall state of moral values is poor would be unusual because the probability is less than 0 .05.
08:06
So that was the first question.
08:08
Now we want to go on to the second question...