Question

The average rent in a city is $1500 per month with a standard deviation of $250. Assume rent follows the normal distribution. Use the empirical rule to answer the following questions.

a. what percentage of rents are between 1250 and 1750?

b. what percentage of rents are less than 1250?

c. what percentage of rents are greater than 2000?

Answer 1

Solution:

According to the empirical rule, we know that about 68% of the data lies within one standard deviations from the mean. About 95% of the data lies within two standard deviations from the mean. About 99.7% of the data is lies within three standard deviations from the mean.

We are given

Mean = 1500

SD = 250

Mean ± 1*SD = 1500 ± 1*250 = (1250, 1750)

About 68% of the data lies within 1250 and 1750.

Mean ± 2*SD = 1500 ± 2*250 = (1000, 2000)

About 95% of the data lies within 1000 and 2000.

Mean ± 3*SD = 1500 ± 3*250 = (750, 2250)

About 99.7% of the data lies within 750 and 2250.

a. what percentage of rents are between 1250 and 1750?

Answer: 68%

(From above explanation regarding empirical rule)

b. what percentage of rents are less than 1250?

Answer: 16%

Explanation:

P(X<1250) = (1 – 0.68)/2 = 0.16 or 16%

(We divide by 2 because distribution is symmetric and upper tail and lower tail has same probability.)

c. what percentage of rents are greater than 2000?

Answer: 2.5%

Explanation:

P(X>2000) = (1 – 0.95)/2 = 0.05/2 = 0.025 or 2.5%

(We divide by 2 because distribution is symmetric and upper tail and lower tail has same probability.)