The Bureau of Labor Statistics' American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged .15 hour (9 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends:

Less than 8 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.)

Proportion _____ and _____

More than two hours. (Round your answers to 4 decimal places.)

Proportion ____ and ____

Between 16 minutes and 48 minutes using a computer for leisure
Proportio ____ and ____

Find the 30th percentile. Seventy percent spend more than what amount of time? (Round your answers to 2 decimal places.)

Amount of time for individuals age 75 and over minutes
Amount of time for individuals ages 15 to 19 minutes

Solution Summary

Step by step method for computing Probability based on exponential distribution is given in the answer.

An infestation of a certain species of caterpillar called the spruce budworm can cause extensive damage to the timberlands of the northern United States. It is known that an outbreak of this type of infestation occurs, on the average, every 30 years.
Assuming that this phenomenon obeys an exponentialprobability law, what is

Consider the following exponential probability density function:
F(x) = (1/14)e^(-x/14) for x>=0
This number represents the time between arrivals of customers at the drive-up window of a bank.
a. Find f(x<=7)
b. Find f(3.5<=x<=7)

The time between arrivals of customers at the drive-up window of a bank follows an exponentialprobabilitydistribution with a mean of 10 minutes.
a. What is the probability that the arrival time between customers will be 7 minutes or less?
b. What is the probability that the arrival time between customers will be between 3 an

Suppose a worker needs to process 400 items. The time to process each item is exponentially distributed with a mean of 2 minutes, and the processing times are independent. Approximately, what is the probability that the worker finishes in less than 7 hours?

Please give step-by-step process for solving the following probability problems.
Let X ~ Exp(lamda1) and that Y ~ Exp(lambda2).
Further assume that X and Y are independent.
(a) Write down the joint pdf (probability distribution function) of X and Y, fXY(x,y).
(b) For t > 0, prove that P(Y < tX) = t lambda2 / ( lambda1 +

At a certain bank, the amount of time that a customer spends being served bya teller is an exponential random variable with mean 5 minutes. If there is a customer in service when you enter the bank, what is the probability that he or she will still be with the teller after an additional 4 minutes?

See attached file.
Suppose that X_i has an exponential distribution with a parameter lamda_i > 0. How do a series of exponentialdistribution functions with distinctive pairwise of random variable X and lamda (ie X_1 and lamda_1, X_2 and lamda_2,..., X_n and lamda_n) be transformed into a beta distribution function?
Note:

Please see attached file for full problem description.
The maintenance department of a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500hours. Let x denote the time (in hours) between successive breakdowns.
a. Find lambda and mu(x)

1. The useful life of an electrical component is exponentially distrbuted with a mean of 2500 hours.
(a) what is the probability the circuit will last more than 3000 hrs.
(b) what is the probability the circuit will last between 2500 and 2750 hours
(c ) what is the probability the circuit will fail within the first 2000 hr