00:01
So we are assuming that the variable x has a normal distribution here with a mean 70 and the variance equals to 81, which means that the standard deviation, which is the square root of the variance, is 9.
00:17
So in item a, we need to find what is the probability that x will be greater than 80.
00:24
So because we have normality, we can use the ze score method to complete this probability, which basically, changes the distribution to be the standard normal distribution.
00:35
And to compute this now, we should compute the z score related to this number, which is given by the number minus the mean, divided by the standard deviation.
00:47
So this means the z should be greater than 1 .11.
00:53
So using the z table that provides the area under the curve for this standard normal distribution, this will give us the probability 013.
01:05
Now for item b, we want to find the probability that x will be between 55 and 82.
01:13
So again, using the z score method here, we need to subtract from each value the mean and divide this difference by the standard deviation to change the distribution to being the standard normal distribution.
01:28
So basically, we should do this for both.
01:31
Values, then what we're going to have is that should be between 167 and 133.
01:42
So using the standard normal distribution, this will give us 0 .86.
01:47
Because basically this here can be open as z being less or equal than the value in the right side, minus the probability of z being less or equal than the value in the left side here.
02:04
So when we find this and this using the z table, you're going to get the difference between these two probability 0 .86.
02:13
Now for item c, we want the probability that x is less than 5 or 75.
02:21
So this means that again using the z score, this is 75 minus 70, divided by 9, which is the probability of z being less than 0 .15.
02:35
So using the z table, this gives us this probability.
02:42
Now in item d, we need to find what is the value of the probability here? so if you know that the probability that x will be greater than a little x is 0 .3.
03:00
This means that this is the same as saying that the probability of x being less than little x is 1 minus 0 .3, which is 0 .7.
03:11
So now we can find the value of z that has the same area.
03:18
So it's the same as same that we want to find the value of z here, which is less than little z, which has this probability.
03:28
So imagine that this is the distinct denominator distribution, and the little z is here, and this area is 0 .7...