1. Given the probability distributions shown to the right, complete the following parts.
| Distribution A: X |
Distribution A: P(X) |
Distribution B: X |
Distribution B: P(X) |
| 0 |
0.03 |
0 |
0.52 |
| 1 |
0.08 |
1 |
0.2 |
| 2 |
0.17 |
2 |
0.17 |
| 3 |
0.2 |
3 |
0.08 |
| 4 |
0.52 |
4 |
0.03 |
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
2. The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts (a) and (b) to the right.
| Number of Accidents Daily(X) |
P(X) |
| 0 |
0.31 |
| 1 |
0.34 |
| 2 |
0.12 |
| 3 |
0.08 |
| 4 |
0.07 |
| 5 |
0.05 |
| 6 |
0.03 |
a. Compute the mean number of accidents per day.
b. Compute the standard deviation.
3. The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) are shown to the right.
| Number Approved |
Frequency |
| 0 |
14 |
| 1 |
25 |
| 2 |
33 |
| 3 |
16 |
| 4 |
9 |
| 5 |
5 |
| 6 |
1 |
| 7 |
1 |
a. Compute the expected number of mortgages approved per week.
b. Compute the standard deviation.
4. You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the probability distribution shown to the right. Complete parts (a) through (c) below.
| Probability |
Economic condition |
Stock X |
Stock Y |
| 0.1 |
Recession |
-80 |
-130 |
| 0.2 |
Slow growth |
20 |
40 |
| 0.4 |
Moderate growth |
100 |
140 |
| 0.3 |
Fast growth |
150 |
210 |
a. Compute the expected return for stock X and for stock Y.
b. Compute the standard deviation for stock X and for stock Y.
c. Would you invest in stock X or stock Y? Explain. Choose the correct answer below.
5. For n = 4 and Π = 0.50, what is P(X=2)?
6. Determine the mean and standard deviation of the variable X in the binomial distribution where n=4 and Π=0.80.
7. A recent survey reported that 63% of 18- to 29-year-olds in a certain country own tablets. Using the binomial distribution, complete parts? (a) through (e) below.
a. What is the probability that in the next six 18- to 29-year-olds surveyed, four will own a tablet?
b. What is the probability that in the next six 18- to 29-year-olds surveyed, all six will own a tablet?
c. What is the probability that in the next six 18- to 29-year-olds surveyed, at least four will own a tablet?
d. What are the mean and standard deviation of the number of 18- to 29-year-olds who will own a tablet in a survey of six?
e. What assumptions do you need to make in (a) through (c)? Select all that apply.
8. Suppose that you and two friends go to a restaurant, which last month filled approximately 91.3% of the orders correctly. Complete parts (a) through (d) below.
a. What is the probability that all three orders will be filled correctly?
b. What is the probability that none of the three orders will be filled correctly?
c. What is the probability that at least two of the three orders will be filled correctly?
d. What are the mean and standard deviation of the binomial distribution used in (a) through? (c)? Interpret these values.
9. Assume a Poisson distribution.
a. If λ =2.5, find P(X=8).
b. If λ =8.0, find P(X =66).
c. If λ =0.5, find P(X =11).
d. If λ =3.7, find P(X =77).
10. Assume a Poisson distribution. Find the following probabilities.
a. Let λ =6.0, find P(X≥2).
b. Let λ =0.6, find P(X≤1).
c. Let λ =6.0, find P(X≤3).
11. Assume a Poisson distribution with λ =4.7. Find the following probabilities.
a. X=1
b. X<1
c. X>1
d. X≤1