Question

The market research department of the National Real Estate Company conducted a survey among 500 prospective buyers in a suburb of a large metropolitan area to determine the maximum price a prospective buyer would be willing to pay for a house. From the data collected, the distribution that follows was obtained. Maximum Price Considered, x (in thousands of dollars) P(X = x) 480 10 500 490 20 500 500 70 500 510 80 500 520 75 500 550 95 500 580 90 500 600 55 500 650 5 500 Compute the mean, variance, and standard deviation of the maximum price x that these buyers were willing to pay for a house. (Round your answer for standard deviation to the nearest dollar.) mean dollars variance dollars2 standard deviation dollars

          The market research department of the National Real Estate
Company conducted a survey among 500 prospective buyers in a suburb
of a large metropolitan area to determine the maximum price a
prospective buyer would be willing to pay for a house. From the
data collected, the distribution that follows was obtained.
Maximum Price
Considered, x
(in thousands of dollars)
P(X = x)
480
10
500
490
20
500
500
70
500
510
80
500
520
75
500
550
95
500
580
90
500
600
55
500
650
5
500
Compute the mean, variance, and standard deviation of the
maximum price x that these buyers were willing
to pay for a house. (Round your answer for standard deviation to
the nearest dollar.)
mean    
  dollars
variance    
 dollars2
standard deviation    
  dollars

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Added by Thomas E.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Donna Densmore

09/08/2023

Step 1

The mean can be found by multiplying each maximum price (x) by its probability (P(X = x)) and then summing up the results. Mean = Σ[x * P(X = x)] Mean = (480 * 10/500) + (490 * 20/500) + (500 * 70/500) + (510 * 80/500) + (520 * 75/500) + (550 * 95/500) + (580 * Show more…

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The market research department of the National Real Estate Company conducted a survey among 500 prospective buyers in a suburb of a large metropolitan area to determine the maximum price a prospective buyer would be willing to pay for a house. From the data collected, the distribution that follows was obtained. Maximum Price Considered, x (in thousands of dollars) P(X = x) 480 10 500 490 20 500 500 70 500 510 80 500 520 75 500 550 95 500 580 90 500 600 55 500 650 5 500 Compute the mean, variance, and standard deviation of the maximum price x that these buyers were willing to pay for a house. (Round your answer for standard deviation to the nearest dollar.) mean dollars variance dollars2 standard deviation dollars

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Transcript

00:01 We have a mean of 365 ,000 and we have a standard deviation of 42 ,000.

00:07 We want to know the coefficient of variation, which is going to be the standard deviation divided by the mean times 100.

00:14 So let's go ahead and go 4 ,200 over 3 ,650 ,000 times 100.

00:21 I like to get rid of zeros, so get rid of those, those.

00:24 So basically we're going to take 4 ,200 divided by 365 and we'll have that coefficient to be 1 .15.

00:33 Now we want to use the empirical rule to determine the range of prices that includes 68 % of the homes and then 68 % of the homes.

00:49 Okay, that's what i'm looking at.

00:50 The z, okay, i've got to go back to my list.

00:53 The z score.

00:53 So let's get our z score for a house that's 382.

00:58 So we want to know our z score, which is going to be the data point minus the mean over the standard deviation.

01:05 So we're looking at 382 ,000 minus the mean, 365, over my standard deviation, 4 ,200.

01:13 So let's go get that number real quick, 365, and then divide that by 4 ,200.

01:20 We get a z score of 4 .05.

01:24 What's the next one we want? we want to know the range for those in the 68%, which is plus or minus one standard deviation of the mean.

01:35 So we're going to take 365 plus or minus 4 ,200...

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