The selling prices for homes in a certain community are...

The selling prices for homes in a certain community are approximately normally distributed with a mean of $321,000 and a standard deviation of $38,000. Estimate the percentage of homes in this community with selling prices (a) between $283,000 and $359,000. % (b) above $359,000. % (c) below $207,000. % (d) between $207,000 and $359,000. %

Transcript

00:02 Hello, so i'm going to answer your question about the specific values, prices, of houses and the specific way to solve it using the natural normal distribution.

00:12 For doing so, first i write down the parameters here, so you have that the mean it's 3 ,000, 3 ,00021, and that the standardization is 308 ,000.

00:23 For solving the problem, this is the formula for a normal distribution where x is the specific value that you want to evaluate, mew is the mean of the population and you divide that by the standard deviation.

00:36 So first they are you, what are the chances that x is between 2 ,8003 and 359 ,000.

00:52 For doing so, first i find the value for the lower bound.

00:56 So i standardize it with this formula that is subtracting the mean and dividing the standardization.

01:02 And this gives me minus 1.

01:04 The issue is that for finding the value that is that seta is above minus 1, i can use it because the table normally give me the value that is the other way around, that seta is bigger than minus 1, so i need to find the complement.

01:19 What i do is because this value is given by the table, i just subtract this value to 1.

01:25 So this value that is given by the table is subtracted to 1 and give me 0 .842.

01:30 Now i try to work with the upper bound.

01:33 With the upper bound i just need to standardize it again so what i did is subtract the mean and divide by the standard deviation and give me again minus 1 but in this case as i told you before ceta just give me the table just give me when the cita is bigger than this value or in this case it's just going to i'm going to use symmetry so the probability that cita is bigger than 1 and it's going to be 0 .158 and then i just subtract this value so i have already the value of x bigger than 2 ,8003.

02:10 And this is the value, and then i subtract the value of the lower band.

02:16 And then i have the final value, so just to give you a quick idea how would graphically be.

02:22 So i want to know first the value that is bigger than minus 1, so it's this value, and this give me this part, and then i want to subtract the part that is bigger than minus 1, but because this curve is symmetric so i just subtract this side that is bigger than one and this area that is with the horizontal lines is the one that i measure and that's the 0 .684...

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