The average rent in a city is 1500 per month with a standard...

The average rent in a city is $1,500 per month with a standard deviation of $250. Assume rent follows the normal distribution. [You may find it useful to reference the z table.] a. What percentage of rents are between $1,250 and $1,750? (Round your answer to 2 decimal places.) b. What percentage of rents are less than $1,250? (Round your answer to 2 decimal places.) c. What percentage of rents are greater than $2,000? (Round your answer to 2 decimal places.)

Transcript

00:01 Now here in this question, you look at the rent in the city, right? now the question says that the rent in the city follows a normal distribution.

00:11 So suppose x denotes the rent and then follows a normal distribution with a mean, which is 1 ,500 and the standard deviation 250.

00:23 Now you ask a few questions, right? the first question to ask you, what percentage of rent are between 1 to 50? and 1 ,750.

00:32 So basically, you ask the percentage for x less than 1 ,750, and larger than 1 ,250, right? well, if you look at the distribution of x, we know that it follows a standard normal distribution, which is a bare -shaped and symmetric, right? so i do not do it pretty well, let me do it better, something like this, right? and the average is somewhere here, right? 1 500, and then 1 -250 is somewhere here.

01:07 1 -750 must be somewhere here.

01:10 So you ask the percentage which of course is given by the area if between these two endpoints under this curve.

01:17 Well, if you denote the area, which is here by alpha, and you can see that because these two end points actually once 250 and it's 1 ,750, actually this to end up, 50, endpoints are symmetric about the mean value.

01:34 So you can see that this area is also alpha, right? now this blue area, and course, which is the percentage is 1 minus 2 alpha, right? so the result is 1 minus 2 alpha.

01:45 Now you need to find all of our.

01:46 Well, the alpha is basically the d score, right? you can find out of our from the d score.

01:53 Now the d squared alpha is simply given by 1 ,500 minus 1 ,250, divided by the standard deviation, which is 250.

02:02 Now, actually, that's actually wrong, right? and you need to look up with the z table to find this alpha value...

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