Purchase Solution

Probability : Random Variables, Gamma, Exponential and Lognormal Distributions

Not what you're looking for?

Ask Custom Question

1. Suppose that family incomes in a town are normally distributed with a mean of $1,200 and a standard deviation of $600 per month. The probability that a given family has an income over $2,000 per month is

Answer: 0.0918

2. If X is a normal random variable with a mean of 15 and a standard deviation of 3, then P(X = 18) is

Answer: 0.0000

3. If telephone calls arrive at a computer telephone service on the average of 30 calls per hour in accordance with a Poisson process, what is the probability that the computer operator will have to wait less than 9.39 minutes for the next nine calls to arrive.

Answer: 0.0500

4. A canning company that cans pineapple juice has a machine that automatically fills 16-ounce cans. From quality control data it was found that the average amount of pineapple juice dispensed into the cans was sixteen ounces with a standard deviation of one ounce. If the amount of fill per can is assumed to be normally distributed, what is the probability that the machine will overfill any of the cans?

Answer: 0.5000

5. If a random variable X is uniformly distributed over the interval [a, b], then the variance for X is
Answer:

6. A rock crushing company has three plants, all receiving blasted rocks in bulk. The amount of rocks that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume that the plants operate independently of each other. How many tons of blasted rocks should be stored at any of the plants per day such that the probability of running out of blasted rocks to crush is 0.05?

Answer: 11.98 tons

7. A certain electronic system has a life with an exponential distribution and with mean of 1000 hours. This system is supported by an identical system. The backup system takes over immediately when the system in operation fails. Assume that the systems are operating independently of each other, then the average for the total life of the main and the backup systems is

Answer: 2000 hours

Attachments
Purchase this Solution

Solution Summary

Probability, Random Variables, Gamma, Exponential and Lognormal Distributions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.