A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes.a) What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order? (Explain/show how you obtain your answer.) (7 pts.)b) What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order? (Explain/show how you obtain your answer.) (7 pts.)c) Find the waiting time at which only 10% of the customers will continue to hold. (Explain/show how you obtain your answer.) (6 pts.)Question 4. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.a) What proportion of the plan recipients would receive payments beyond age 75? (Explain/show how you obtain your answer.) (7 pts.)b) What proportion of the plan recipients die before they reach the standard retirement age of 65? (Explain/show how you obtain your answer.) (7 pts.)c) Find the age at which payments have ceased for approximately 86% of the plan participants. (Explain/show how you obtain your answer.) (6 pts.)