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?

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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.

  1. What is the probability of the case that 44 out of 547 will be likely laid off?
  2. What is the probability of the case that more than 44 out of 547 will be likely laid off?
Expert Solution
Step 1

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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