A labor statistician claims that 6% of the labor forces will be laid off likely to pandemic impact. In a random sample of 547 employees, 44 of them will be likely to be laid off. What is the probability of the case that 44 out of 547 will be likely laid off? What is the probability of the case that more than 44 out of 547 will be likely laid off?
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.
A labor statistician claims that 6% of the labor forces will be laid off likely to pandemic impact. In a random sample of 547 employees, 44 of them will be likely to be laid off.
- What is the
probability of the case that 44 out of 547 will be likely laid off? - What is the probability of the case that more than 44 out of 547 will be likely laid off?
Solution:
According to the labor statistician's claim, 6% of the labor forces will be laid off likely to pandemic impact.
Let p be the probability that labor forces will be paid off. p = 0.06
Sample size: n = 547
Part 1)
Let X be the random variable defined as the number of labor who will be paid off.
The probability that 44 out of 547 will be likely laid off is required. It can be written as P(X =44)
X follows Binomial distribution with n = 547 and p = 0.06.
The required probability can be easily found using MS-Excel.
Type =BINOMDIST(44,547,0.06,0) and hit enter, it gives 0.009931.
Thus, the probability of the case that 44 out of 547 will be likely laid off is 0.009931.
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