Discuss the below:
Q1: Assume that you are the owner of a small business that employs two people on a telephone help desk. Records show that one of the employees is busy taking calls for 40% or the time and the other is busy taking calls 55% of the time:
a) What is the probability that when a new call comes in that both of the employees are busy on the telephone?
b) What is the probability that at least one of the employees will be available?
Q2: Venture capital investments tend to be risky investments with a large proportion of investments being unsuccessful. Suppose that you are the manager of a venture capital firm with 20 investments. Assuming that it is known that 70% of venture capital investments will be unsuccessful, determine the following:
a) The probability that at least 5 of your investments will be successful.
b) The probability that no more than 15 will be unsuccessful.
Q3: Suppose that 22% of employees in Australia intend to change employers over the next two years. A company interested in reasons for their employee turnover randomly samples a number of their employees:
a) If the company randomly samples 20 employees, find the probability that exactly 4 of them will leave within two years.
b) For a random sample of 20 employees, find the mean, the variance and the standard deviation for the number of employees that intend to change employers of the next two years.