Question

Among the 120 applicants for a job, only 80 are qualified. If 5 of these applicants are randomly selected for an interview, answer the following:

a. Identify the random process

b. Define a variable

c. Associate the random variable with a distribution and its parameters

Solve using Rstudio:

d. Find the probability that exactly 2 of the 5 are qualified for the job
e. Find the probability that at least 3 of the 5 are qualified for the job
f. Find the probability that at most 4 of the 5 are qualified for the job.

Answer 1

The probability that the selected applicant is qualified is

1) The random process is Binomial.

b) The Random variable is . X can take values 0,1,2,3,4,5.

c) The distribution is Binomial with parameters

.

Consider the following MINITAB screenshot (Choose "Calc" ->Probability Distribution ->Binomial)

d) The probability that exactly 2 of the 5 are qualified for the job is   0.164576.

e) The probability that at least 3 of the 5 are qualified for the job is 1-0.209827 = 0.790173 

f) The probability that at most (at most) 4 of the 5 are qualified for the job is 0.868280

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