The average rent in a city is $1,580 per month with a standard deviation of $270

Question

The average rent in a city is $1,580 per month with a standard deviation of $270. Assume rent follows the normal distribution. Use the empirical rule for normal distributions to answer the following questions.

a. What percentage of rents are between $1,040 and $2,120?

(Round your answer to the nearest whole percent.) Percentage of rents

b. What percentage of rents are less than $1,040?

(Round your answer to 1 decimal place.) Percentage of rents

c. What percentage of rents are greater than $2,390?

(Round your answer to 1 decimal place.) Percentage of rents

Explanation / Answer

Solution:

Given in the question

Mean = 1580

SD= 270

Solution1: we have to find

P(1040<x<2120)

First we will find Z value

Z= (1040-1580)/270

Z= -540/270

Z=-2

Z= 2120-1580 /270

Z= 2

P(1040<x<2120) = P(x<2120)-P(X<1040)

P(1040<x<2120) = 0.9772 - 0.0228

P(1040<x<2120)= 0.9554 or 95.54%

Solution 2:

P(X<1040) for Z= -2 from Z table

P(X<1040)= 0.0228 which is 2.28%

Solution 3:

P(x>2390)

Z= 2390-.1580 / 270

Z= 810/270

Z= 3

P(X>2390)=1-p(x<2390)

P(x>2390)= 1- 0.9987

= 0.0013 or 0.13%

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