Concept explainers
a.
Create a probability distribution for the number of travelers who plan their trips within two weeks of departure.
a.
Answer to Problem 53CE
The probability distribution for the number of travelers who plan their trips within two weeks of departure is as follows:
Number of travelers | Probability |
0 | 0.0001 |
1 | 0.0019 |
2 | 0.0116 |
3 | 0.0418 |
4 | 0.1020 |
5 | 0.1768 |
6 | 0.2234 |
7 | 0.2075 |
8 | 0.1405 |
9 | 0.0676 |
10 | 0.0220 |
11 | 0.0043 |
12 | 0.0004 |
Explanation of Solution
The formula to find the binomial probability is as follows:
Let x denotes the travelers who plan their trips within two weeks of departure.
Here, n=12;
For the number of traveler
Similarly the probability value for the remaining x values is calculated.
Thus, the probability distribution for the number of travelers who plan their trips within two weeks of departure is obtained as follows:
Number of travelers | Probability |
0 | |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 | |
11 | |
12 |
b.
Compute the mean and standard deviation for the given distribution.
b.
Answer to Problem 53CE
The mean is 6.24.
The standard deviation is 1.7307.
Explanation of Solution
The mean and standard deviation of the binomial distribution are as follows:
The mean of the distribution is calculated as follows:
Therefore, the mean of the distribution is 6.24.
The standard deviation of the distribution is calculated as follows:
Therefore, the standard deviation of the distribution is 1.7307.
c.
Compute the probability of exactly 5 of the 12 selected business travelers plan their trips within two weeks of departure.
c.
Answer to Problem 53CE
The probability of exactly 5 of the 12 selected business travelers plan their trips within two weeks of departure is 0.1775.
Explanation of Solution
The probability of exactly 5 of the 12 selected business travelers plan their trips within two weeks of departure is calculated as follows:
Therefore, the probability of exactly 5 of the 12 selected business travelers plan their trips within two weeks of departure is 0.1775.
d.
Compute the probability that 5 or fewer of the 12 selected business travelers plan their trips within two weeks of departure.
d.
Answer to Problem 53CE
The probability that 5 or fewer of the 12 selected business travelers plan their trips within two weeks of departure is 0.3343.
Explanation of Solution
The probability that 5 or fewer of the 12 selected business travelers plan their trips within two weeks of departure is calculated as follows:
Therefore, the probability that 5 or fewer of the 12 selected business travelers plan their trips within two weeks of departure is 0.3343.
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Chapter 6 Solutions
STATISTICAL TECHNIQUES FOR BUSINESS AND
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill