Recall that the binomial distribution with parameters n, p, and r gives the probability distribution of the number of r successes in a sequence of n trials, each of which yields success with probability p. The Binomial Probability Distribution table can be used to find probabilities associated with the binominal distribution. A portion of this table is displayed below. p n r 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 5 0 0.951 0.774 0.590 0.444 0.328 0.237 0.168 0.116 0.078 0.050 0.031 1 0.048 0.204 0.328 0.392 0.410 0.396 0.360 0.312 0.259 0.206 0.156 2 0.001 0.021 0.073 0.138 0.205 0.264 0.309 0.336 0.346 0.337 0.313 3 0.000 0.001 0.008 0.024 0.051 0.088 0.132 0.181 0.230 0.276 0.313 4 0.000 0.000 0.000 0.002 0.006 0.015 0.028 0.049 0.077 0.113 0.156 5 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.005 0.010 0.018 0.031 Use the table to find P(r = 0), when n = 5 and p = 0.05 correct to three decimal places. a) P(r = 0) = ______
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Recall that the binomial distribution with parameters n, p, and r gives the
The Binomial Probability Distribution table can be used to find probabilities associated with the binominal distribution. A portion of this table is displayed below.
| p | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| n | r | 0.01 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 |
| 5 | 0 | 0.951 | 0.774 | 0.590 | 0.444 | 0.328 | 0.237 | 0.168 | 0.116 | 0.078 | 0.050 | 0.031 |
| 1 | 0.048 | 0.204 | 0.328 | 0.392 | 0.410 | 0.396 | 0.360 | 0.312 | 0.259 | 0.206 | 0.156 | |
| 2 | 0.001 | 0.021 | 0.073 | 0.138 | 0.205 | 0.264 | 0.309 | 0.336 | 0.346 | 0.337 | 0.313 | |
| 3 | 0.000 | 0.001 | 0.008 | 0.024 | 0.051 | 0.088 | 0.132 | 0.181 | 0.230 | 0.276 | 0.313 | |
| 4 | 0.000 | 0.000 | 0.000 | 0.002 | 0.006 | 0.015 | 0.028 | 0.049 | 0.077 | 0.113 | 0.156 | |
| 5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.001 | 0.002 | 0.005 | 0.010 | 0.018 | 0.031 |
Use the table to find P(r = 0), when n = 5 and p = 0.05 correct to three decimal places.
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