Exercises. 1. Let x be a continuous random variable that possesses an exponential probability distribution with

1. Let x be a continuous random variable that possesses an exponential probability distribution with . Find the following probabilities

a) ; b) ; c)

2. The life of a pie is exponentially distributed with a mean of three days. What is the probability that a pie that is baked just now will still be good after four days?

3. At the supermarket, a customer has to wait an average of four minutes in line before being served. The time a customer has to wait is exponentially distributed.

a) What is the probability that a customer will have to wait for more than eight minutes in line?

b) What is the probability that a customer will have to wait for three to seven minutes in line?

4. On average, 20 telephone calls are received per hour at an office. The time between calls received at this office is exponentially distributed.

a) What is the probability that no calls will come in during the next 10 minutes?

b) What is the probability that the next call will come in within 4 minutes?

5. Aysel works for a toy company and assembles five toys per hour on average. The assembly time for this toy follows an exponential distribution.

a) Find the probability that the next toy will take more than 15 minutes to assemble.

b) What is the probability that the next toy will take less than 8 minutes to assemble?

c) What is the probability that the next toy will take 10 to 16 minutes to assemble?

6. A student, working in a part time job, sells life insurance policies. The past data show that he (she) sells, on an average, 10 life insurance policies per 4-week period. Assume that the time between successive sales of life insurance policies by student has an exponential distribution.

a) What is the probability that the next life insurance policy will not be sold for two weeks?

b) What is the probability that the next life insurance policy will be sold within one week?

c) What is the probability that the next life insurance policy will sold in one to two weeks?

Дата добавления: 2015-08-05