Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials. (a) Compare P(3 successes), where p = 0.30, with P(2 successes), where p = 0.70. P(3 successes), where p = 0.30, is larger.P(3 successes), where p = 0.30
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.
Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials.
(b) Compare P(3 or more successes), where p = 0.30, with P(2 or fewer successes), where p = 0.70.
(c) Find the value of P(4 successes), where p = 0.30. (Round your answer to three decimal places.)
P(4 successes) =
For what value of r is P(r successes) the same using p = 0.70?
r =
(d) What column is symmetrical with the one headed by p = 0.20?
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