Solution Found!
Housing The following probability model shows the
Chapter 4, Problem 30AYU(choose chapter or problem)
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.