According to a survey by the Administrative Management Society, one-half of U. S. companies give employees 4 weeks of vacation after they have been with the company for 15 years. Find the probabil- ity that among 6 companies surveyed at random, the number that give employees 4 weeks of vacation after 15 years of employment is

a

b

Step-by-step explanation:

Let the random X variable representing the 6 companies that give 4 weeks of vacation after 15 years of employment:

-let p=0.5 be the probability of vacation. Since the companies are independent, X assumes a binomial random variable:

#Probability that the number of companies that give vacation is anywhere from 2 to 5:

We use equation 1;

Hence the probability that between 2 and 5 companies give vacation is 0.875

b. The probability that fewer than 3 companies give vacation is calculated as:

From equation one we get:

Hence the probability that less than three companies give vacation is 0.3432

1.0

step-by-step explanation: