Concept explainers
a.
Create a
a.
Answer to Problem 52CE
The probability distribution for the number of students in the sample who watch soap operas is as follows:
Number of students | Probability |
0 | 0.0025 |
1 | 0.0207 |
2 | 0.0763 |
3 | 0.1665 |
4 | 0.2384 |
5 | 0.2340 |
6 | 0.1596 |
7 | 0.0746 |
8 | 0.0229 |
9 | 0.0042 |
10 | 0.0003 |
Explanation of Solution
The formula to find the binomial probability is as follows:
Let x denotes the students who watch soap operas.
Here, n=10;
For the number of students
Similarly the probability value for the remaining x values is calculated.
Thus, the probability distribution for the number of students in the sample who watch soap operas is obtained as follows:
Number of students | Probability |
0 | |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 |
b.
Compute the mean and standard deviation of this distribution.
b.
Answer to Problem 52CE
The mean is 4.5.
The standard deviation is 1.5732.
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 4.5.
The standard deviation of the distribution is calculated as follows:
Therefore, the standard deviation of the distribution is 1.5732.
c.
Compute the probability of finding exactly four students who watch soap operas.
c.
Answer to Problem 52CE
The probability of finding exactly four students who watch soap operas is 0.2384.
Explanation of Solution
The probability of finding exactly four students who watch soap operas is calculated as follows:
Therefore, the probability of finding exactly four students who watch soap operas is 0.2384.
d.
Compute the probability that less than half of the students selected watch soap operas.
d.
Answer to Problem 52CE
The probability that less than half of the students selected watch soap operas is 0.5044.
Explanation of Solution
The probability that less than half of the students selected watch soap operas is calculated as follows:
Therefore, the probability that less than half of the students selected watch soap operas is 0.5044.
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