(a)
To describe: The shape of the binomial distribution of exactly
Shape of the distribution is skewed.
Given information:
Number of trail is 5.
Formula used:
Probability of a certain event can be found by the following formula:
Formula of Binomial distribution of
Shape of the distribution will be symmetric if left half of the distribution is the mirror image of right half.
Shape of the distribution will be skewed if the distribution is not symmetric about any vertical line.
Calculation:
Here, number of randomly chosen family is 5.
Success probability is 0.4.
The probability distribution is shown below:
The binomial distribution table is shown below:
Binomial distribution | |
0 | 0.07776 |
1 | 0.2592 |
2 | 0.3456 |
3 | 0.2304 |
4 | 0.0768 |
5 | 0.01024 |
The histogram for the probability distribution is shown below:
Shape of the distribution will be skewed since the distribution is not symmetric about any vertical line.
(b)
To describe: The shape of the binomial distribution of exactly
Shape of the distribution is symmetric.
Given information:
Number of trail is 5.
Formula used:
Probability of a certain event can be found by the following formula:
Formula of Binomial distribution of
Shape of the distribution will be symmetric if left half of the distribution is the mirror image of right half.
Shape of the distribution will be skewed if the distribution is not symmetric about any vertical line.
Calculation:
Here, number of randomly chosen family is 5.
Success probability is 0.5.
The probability distribution is shown below:
The binomial distribution table is shown below:
Binomial distribution | |
0 | 0.03125 |
1 | 0.15625 |
2 | 0.3125 |
3 | 0.3125 |
4 | 0.15625 |
5 | 0.03125 |
The histogram for the probability distribution is shown below:
Shape of the distribution will be symmetric since left half of the distribution is the mirror image of right half..
Chapter 6 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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