M/PF Research, Inc. lists the average monthly apartment rent in some of the most

Question

M/PF Research, Inc. lists the average monthly apartment rent in some of the most expensive apartment rental locations in the United States. According to their report, the average cost of renting an apartment in Minneapolis is $951. Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed. If a Minneapolis apartment is randomly selected, what is the probability that the price is:

(Round the values of z to 2 decimal places. Round answers to 4 decimal places.)

(a) $1,030 or more?

(b) Between $920 and $1,090?

(c) Between $830 and $920?

(d) Less than $720?

Explanation / Answer

In this normal distribution problem, the mean is 951 and standard deviation is 96

a) P(x>1030)= P(z>(1030-951)/96)=P(z>0.82) or 1-P(z<0.82). from the normal distribution table we get 1-0.7939=0.2061

b) P(920<x<1090)= P((920-951)/96<z<(1090-951)/96)=P(-0.32<z<1.45)=P(z<1.45)-(1-P(z<0.32)). from normal table we get 0.9265-(1-0.6255)= 0.552

c) P(830<x<920)=P((830-951)/96<z<(920-951)/96)=P(-1.26<z<-0.32)=P(z<-0.32)-P(z<-1.26)=P(z<1.26)-P(z<0.32)

From the nromal distribution table we get 0.8962-0.6255= 0.2707

d) P(x<720)= P(z<(720-951)/96)=P(z<-2.41)=1-P(z<2.41) from the normal distribution table 1-0.9920=0.008

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