00:01
We are told that credit scores in america are portrayed by a normal distribution with a mean of 630, a standard deviation of 40, and for question 1, we are asked for the probability that a person will have a credit score less than 600.
00:16
So this is the probability that x is less than 600.
00:21
This graph represents our normal distribution for credit scores.
00:25
We have a mean of 630 in the center.
00:28
600 is approximately here, and the probability that x is less than 600 is equal to the area under the curve and to the left of 600.
00:39
So that corresponds to the area of this blue shaded region.
00:43
Now if we wish to use a standard normal table to solve this probability, we standardize the variable according to this formula.
00:53
So doing that, we have this equal to the probability that z is less than minus .75.
00:59
And then if we look up z equals minus .75 in the standard normal table, that corresponds to a cumulative probability of .2266.
01:16
So the probability of a credit score less than 600 is .2266.
01:24
And for two, we want the probability of a credit score greater than 700.
01:32
This can be expressed as 1 minus the probability that x is at most 700.
01:36
And if we standardize, this is equal to 1 minus the probability that z is less than 1 .75.
01:51
And now looking up, z equals 1 .75 in a standard normal table, that corresponds to a cumulative probability of 0 .9599.
02:09
And this comes out to a probability of 0 .0401.
02:16
And for question 3, you were asked what percentage of people have credit scores between 400 and 720, so this is the probability that x is between 400 and 720.
02:30
And this can be expressed as the probability that x is at most 720, minus the probability that x is less than 400.
02:43
Let's use software this time.
02:44
We can use the normal distribution function in excel, and we'll do both terms in one step.
02:50
So in excel, we start a computation with an equal sign.
02:53
We want to use the normal distribution function, so we select that.
02:58
For the first term, the first argument is 700.
03:01
Then we enter the mean and the standard deviation.
03:04
The cumulative argument is true because we want the probability that x is anything less than 700...