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In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Housing Units. The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands.

A housing unit is selected at random. Find the probability that the housing unit obtained has

(a) four rooms.

(b) more than four rooms.

(c) one or two rooms.

(d) fewer than one room.

(e) one or more rooms.

Short Answer

Expert verified

Part (a) 0.179.

Part (b) 0.720.

Part (c) 0.015.

Part (d) 0

Part (e) 1

Step by step solution

01

Part (a) Step 1. Given information. 

The given statement is:

The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands.

Rooms

No. of units

1

601

2

1,404

3

11,433

4

23,636

5

30,440

6

27,779

7

17,868

8+

19,257

02

Part (a) Step 2. Find the probability that the housing unit obtained has four rooms.

We know that an event's probability ranges from 0 to 1, and both 0 and 1 are included in it.


The formula for the probability of an event is:

P(E)=No.offavorableoutcomesTotalno.ofoutcomes

The total number of housing units in America according to the housing Survey for the United States is 1,32,418.

Therefore, the total number of instances of housing units will become 1,32,418.


The total instances where the housing unit obtained has four rooms is:

23,636

Let's call the occurrence 'E' where the housing unit obtained has four rooms.


The probability that the housing unit obtained has four rooms is:

P(E)=23,6361.32,418=0.179

03

Part (b) Step 1. Find the probability that the housing unit obtained has more than four rooms.

The total instances where the housing unit obtained has more than four rooms is:

30,440+27,779+17,868+19,257=95,344

Let's call the occurrence 'E' where the housing unit obtained has more than four rooms.

The probability that the housing unit obtained has more than four rooms is:

P(E)=95,3441,32,418=0.720

04

Part (c) Step 1. Find the probability that the housing unit obtained has one or two rooms.

The total instances where the housing unit obtained has one or two rooms is:

601+1,404=2,005

Let's call the occurrence 'E' where the housing unit obtained has one or two rooms.

The probability that the housing unit obtained has one or two rooms is:

P(E)=20051,32,418=0.015

05

Part (d) Step 1. Find the probability that the housing unit obtained has fewer than one room.

The total instances where the housing unit obtained has fewer than one room is:

Let's call the occurrence 'E' where the housing unit obtained has fewer than one room.

The probability that the housing unit obtained has fewer than one room is:

P(E)=01,32,418=0

06

Part (e) Step 1. Find the probability that the housing unit obtained has one or more rooms.

The total instances where the housing unit obtained has one or more rooms are:

601+1,404+11,433+23,636+30,440+27,779+17,868+19,257=1,32,148

Let's call the occurrence 'E' where the housing unit obtained has one or more rooms.

The probability that the housing unit obtained has one or more rooms is:

P(E)=1,32,4181,32,418=1

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