810) See Ex. 809. a) Find the probability of obtaining 2 nonconforming units on the first sample of 2 and 1 nonconforming unit on the second sample of 2. b) What is the probability of 0 nonconforming units on the first sample and 1 nonconforming units on the second? The first sample is returned before the second sample is selected. ex 809 It is given that, the probability of obtaining 1 nonconforming unit in a sample of two is 0.39 and the probability of 2 nonconforming units in a sample of two is 0.16. Consider a random variable x that defines the number of nonconforming unit in the sample. Hence, according to question, P(X = 1) = 0.39 and P(X = 2) = 0.16. It is known that the sum of the probabilities is 1. That is, P(X = 0) + P(X = 1) + P(X = 2) = 1 P(X = 0) = 1 – P(X = 1) – P(X = 2) = 1 – 0.39 – 0.16 = 0.45. Thus, the probability of zero nonconforming units in a sample of two is 0.45.
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.
810) See Ex. 809. a) Find the
ex 809
It is given that, the probability of obtaining 1 nonconforming unit in a sample of two is 0.39 and the probability of 2 nonconforming units in a sample of two is 0.16.
Consider a random variable x that defines the number of nonconforming unit in the sample.
Hence, according to question, P(X = 1) = 0.39 and P(X = 2) = 0.16.
It is known that the sum of the probabilities is 1.
That is, P(X = 0) + P(X = 1) + P(X = 2) = 1
P(X = 0) = 1 – P(X = 1) – P(X = 2) = 1 – 0.39 – 0.16 = 0.45.
Thus, the probability of zero nonconforming units in a sample of two is 0.45.
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