Question

The distribution of monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61. A graduate student is looking for a one-bedroom apartment and wants to pay no more than $800 in monthly rent. Of the following, which is the best estimate of the percent of one-bedroom apartments in the city with a monthly rent of at most $800 ?
(A) 1.3%
(B) 2.5%
(C) 50%
(D) 95%
(E) 97.5%

Answer 1

Answer: (A) 1.3%

Step-by-step explanation:

Given: The monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61.

i.e. $\mu=936\ \ \ , \sigma=61$

Let X denotes the monthly rent for one-bedroom apartments.

Required probability = $P(X\leq800)=P(\dfrac{X-\mu}{\sigma}\leq\dfrac{800-936}{61})$

$=P(Z\leq\dfrac{-136}{61})\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z\leq-2.23)\\\\=1-P(Z\leq 2.23)\ \ \ [P(Z$

Hence, the correct option is (A) 1.3%