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

ID: 3055203 • Letter: M

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) $980 or more? (b) Between $900 and $1,110? (c) Between $820 and $915? (d) Less than $690?

Explanation / Answer

mean = 951
sd = 96

a)
P(X > 980)
= P(z > (980 - 951)/96)
= P(z > 0.3021)
= 0.3821

b)
P(900 < X < 1100)
= P((900 - 951)/96 < z < (1100 - 951)/96)
= P(-0.53 < z < 1.55)
= P(z < 1.55) - P(z < -0.53)
= 0.9394 - 0.2981
= 0.6414

c)
P(820 < X < 915)
= P((820 - 951)/96 < z < (915 - 951)/96)
= P(-1.36 < z < -0.38)
= P(z < -0.38) - P(z < -1.36)
= 0.352 - 0.0869
= 0.2651

d)
P(X < 690)
= P(z < (690 - 951)/96)
= P(z < -2.72)
= 0.0033