1 A normal distribution with mean 700 and standard deviation

1. A normal distribution with mean $700 and standard deviation $150 will be used to model the monthly rental rate for 1 BR apartments in a college town.

a) Use the Empirical Rule to ESTIMATE the percent of 1 BR apartments renting between $550 and $850 per month.  %

(b) The probability to the left of $1075 is 0.994. Use this information to answer the following questions.

(i) What is the probability that a 1 BR apartment selected at random will rent for more than $1075?

(ii) What is the probability that a 1 BR apartment selected at random will rent somewhere between $700 and $1075?

2. For the normal distribution shown below, find the probability that an observation falls in the shaded region.

Solution

mean $700

standard deviation $150

z score for 550 = -1

z score for 850 = 1

a) percent required = 68.26%

-------------------------

b) i) 1-0.994 = 0.006

c) 0.494

--------------------------

2) P(Z>0.67) = 0.2514