The average rent in a city is $1,670 per month with a standard deviation of $230

Question

The average rent in a city is $1,670 per month with a standard deviation of $230. Assume rent follows the normal distribution. Use the empirical rule for normal distributions to answer the following questions.

What percentage of rents are between $1,210 and $2,130? (Round your answer to the nearest whole percent.)

  Percentage of rents

What percentage of rents are less than $1,210? (Round your answer to 1 decimal place.)

What percentage of rents are between $1,210 and $2,130? (Round your answer to the nearest whole percent.)

Explanation / Answer

MEAN = 1670

STANDARD DEV = 230

A)

For x = 1210 , z = (1210 - 1670) / 230 = -2 and for x = 2130, z = (2130 - 1670) / 230 = 2

Hence P(1210 < x <2130 ) = P(-2 < z < 2) = [area to the left of z = 2] - [area to the left of -2]

= 0.9772 - 0.0228 = 0.9544

B)

For x = 1210, the z-value z = (1210 - 1670) / 230 = -2

Hence P(x < 1210) = P(z < -2) = [area to the left of -2] = 0.0228

C)

For x = 2360, z = (2360 - 1670) / 230 = 3

Hence P(x > 2360) = P(z > 3) = [total area] - [area to the left of 3]

= 1 - 0.9987= 0.0013

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