00:01
There is given an normal distribution here, and the mean value was given.
00:04
So the mean of the population, which is denoted by mu.
00:07
This is $3 ,500, $3 ,500.
00:13
And the standard division, which is denoted by sigma, that was given as $500.
00:20
So i can just define the random variable here.
00:23
Let's say x be the random variable for this normal distribution.
00:26
This is $3 ,500 and $500.
00:29
So in part a, what we have to do, we have to find more than this value.
00:35
So the probability of random variable x, which is greater than 200, 2 ,750.
00:41
We have to get this probability here.
00:43
So what we have to do, we're going to use the normal cdf function here.
00:48
The lower boundary here, 2750, and there is no in upper boundary here.
00:52
I'm going to put very big number.
00:53
And the mean value is 3500 in the standard division, which is 500.
00:58
Press second and this variance, the normal cdf, lower boundary, which is 2750 comma.
01:05
This is one second in 99, and this is 3 ,500, and the mean standard division, which is 500.
01:13
Let me just erase this one and write clearly.
01:15
This is 500.
01:16
So the probability here, which is 0 .93 and 32, but the question is being asked in the percentage, so i'm going to multiply this by 100.
01:24
We got 93 .32 % 0%.
01:28
The values are greater than 2 ,750 and b, what percentage of residence is exempt from the city? so individuals with incomes less than this one, they are exempt from the city taxes.
01:42
So we have to get the probability of axis less than, which is 24 and 60.
01:49
So again, i'm going to use the normal cdf function.
01:52
So in this case, there is no in a lower boundary.
01:54
I'm going to put very small number, the upper boundary, 2460, and the mean value, and the standard division.
02:01
Great.
02:01
Let's get the answer.
02:03
Press second and variance, the second option here.
02:06
This is negative 1, 2nd, e99, and the upper boundary is 2460.
02:11
This is 3 ,500, and then 500.
02:16
So the answer would be, which is 0 .01 and 88.
02:20
If i just multiply 100, we will get the percentage, which is 1 .88.
02:24
Percent of the residents are less than this value.
02:29
This is 2 ,460.
02:31
And what about for part c? the minimum and the maximum income is for the middle 95%.
02:37
So we can just get used to from the empirical rule.
02:42
Remember what empirical rule says...