Respuesta :
Using the binomial distribution, it is found that the probabilities are given by:
a) 0.8681 = 86.81%.
b) 0.1319 = 13.19%.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem, we have that:
- 98% of the employees are eligible, hence p = 0.98.
- A sample of 7 was taken, hence n = 7.
Item a:
The probability is P(X = 7), hence:
P(X = 7) = 0.98^7 = 0.8681 = 86.81%.
Item b:
The probability is:
P(X < 7) = 1 - P(X = 7) = 1 - 0.8681 = 0.1319 = 13.19%.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
