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Housing The following probability model shows the

Chapter 4, Problem 30AYU

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QUESTION:

Problem 30AYU

Housing The following probability model shows the distribution for the number of rooms in U.S. housing units.

Rooms

Probability

One

0.005

Two

0.011

Three

0.088

Four

0.183

Five

0.230

Six

0.204

Seven

0.123

Eight or more

0.156

(a) Verify that this is a probability model.

(b) What is the probability that a randomly selected housing unit has four or more rooms? Interpret this probability.

(c) What is the probability that a randomly selected housing unit has fewer than eight rooms? Interpret this probability.

(d) What is the probability that a randomly selected housing unit has from four to six (inclusive) rooms? Interpret this probability.

(e) What is the probability that a randomly selected housing unit has at least two rooms? Interpret this probability.

Questions & Answers

QUESTION:

Problem 30AYU

Housing The following probability model shows the distribution for the number of rooms in U.S. housing units.

Rooms

Probability

One

0.005

Two

0.011

Three

0.088

Four

0.183

Five

0.230

Six

0.204

Seven

0.123

Eight or more

0.156

(a) Verify that this is a probability model.

(b) What is the probability that a randomly selected housing unit has four or more rooms? Interpret this probability.

(c) What is the probability that a randomly selected housing unit has fewer than eight rooms? Interpret this probability.

(d) What is the probability that a randomly selected housing unit has from four to six (inclusive) rooms? Interpret this probability.

(e) What is the probability that a randomly selected housing unit has at least two rooms? Interpret this probability.

ANSWER:

Answer:

Step 1

(a) Verify that this is a probability model.

  The Requirements of probability are

   Sum of all the probability must be equal to 1.

   Each value of the probability should lie in between 0 and 1

Rooms

Probability

One

0.005

Two

0.011

Three

0.088

Four

0.183

Five

0.23

Six

0.204

Seven

0.123

Eight or more

0.156

 

1


(b) What is the probability that a randomly selected housing unit has four or more rooms? Interpret this probability.

 P( X 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

                 = 0.183 + 0.23 + 0.204 + 0.123 + 0.156

                 = 0.896.

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