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Probability Theory

Mean, Median, Mode, Distributions and Standard Deviations

1) Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for customers at the bank. Here are the waiting times (in minutes): 11, 21, 17, 9, 12, 23, 7, 5. A) What is the median of

Means & probability

Means & probability The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of

Means & Probability: Queuing Theory

Q1 In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour or 0.6 customer per minute. Use the exponential probability distribution to answer the following questions.

Measures of variation

Pax World Balanced: x with line over it= 9.58%;s= 14.05% Vanguard Balanced Index : x with line over it = 9.02%;s = 12.50% These are the means and standard deviations of annualized percent returns. A) compute the coefficient of variation for each fund. If x (with line over it)represents return and s represents risk, then exp

Introduction to Statistics

Having trouble comprehending the attached questions. Need to complete these tasks for a study guide to final exam. 1 of 9 A medical research team studied the ages of patients who had strokes caused by stress. The ages of 34 patients who suffered stress strokes were as follows. Use 8 intervals starting with 25-29. 29 30 3

Decision theory

See attached notes to solve for problems in the attachment. Show work. 3-17 Although Ken Brown is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob is vice president of finance. Bob attributes his success to his pessimistic attitude about business and the oil in

Functions and Statistical Models

4.30 A team of consultants working for a large national supermarket chain based in the New York metropolitan area developed a statistical model for predicting the annual sales of potential new store locations. x 1 2 3 4 5 6 7 8 9 10 Relative Frequency .01 .04 .04 .08 .10 .15 .25 .20 .08 .05 a) Find E(x) and interpret its valu

Application of Chebyshev's theorem in probability calculation

BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean

Calculation of probability based on Chebyshev's inequality.

1. According to Chebyshev's theorem, at least ________, of the lifetimes lie between 609.5 hrs and 1074.5 hrs. a. 56% b. 75% c. 84% d. 89% 2. According to Chebyshev's theorem, at least ________, of the lifetimes lie between 656 hrs and 1028 hrs. a. 56% b. 75% c. 84% d. 89% 3. Suppose that th

Payoff Table/Decision Situation

The Loebuck Company must decide how many cases of milk to stock each week to meet demand. The probability distribution of demand during a week is shown in the following table. Each case costs the grocer $10 and sells for $12. Unsold cases are sold to a local farmer ( who mixes the milk with feed from livestock) for $2 per case.


1.Management of an airline knows that 0.5% of the airline's passengers lose their luggage on domestic flights. Management also know that the average value claimed for a lost piece of luggage on domestic flights is $600.00. The company is considering increasing fares by an appropriate amount to cover expected compensation to pass

Life insurance policies: EMV criterion

ABC insurance sells term life insurance policies. If the policy holder dies during the term of the policy ABC pays out $100,000. If the person does not die ABC pays nothing and there is no further value to the policy. ABC has determined through actuarial tables that an individual with certain issues has a 0.001 chance that they

Mathematical statistics problems

I can not get the true answers, so I need the step by step solutions for these three questions. My problems and necessary information are in the attached file (one question at each page).

Conceptual Statistics

This question is open to interpretation - I think it's supposed to be a tricky question so I'm not entirely sure where it's going. We aren't actually given any data. Assuming data normally distributed: Q 1 Theoretically, does the nature of the observed data have an effect on the definition of what is called "mild" and

Identify the type of sampling

Please see the attached file. 1. Identify the type of sampling (random, stratified, systematic, cluster, convenience) used in each of the following AND state whether the sample results are likely to reflect the population from which the sample was drawn. (3 points each) a. ______________________ Each hundredth hamburger m


Lex X be a random variable such that P(X<=0)=0 and let mu=E(X) exist. Show that P(X>=2*mu) <= 1/2.

Solving for Inequalities

Question: Let X be a random variable with a mean mu and let E[(X-mu)^2k] exist. Show, with d>0, that P(|X-mu| >=d) <=E[(X-mu)^(2k)]/d^(2k). This is essentially Chebyshev's inequality when k=1.

Digital LPF Using Impulse Invariance Method

See attached word file. Taken from 'Digital Signal Processing Using MatLab' by Ingle/Proakis 1. Design a digital LPF to be used in the configuration To satisfy the following requirements: Sampling rate = 8 kilosamples/sec Passband edge of 1.5kHz with ripple of 3dB Stopband edge of 2kHz with attenuation of 40dB Equiripp

Chebyshev ploynomial of degree 4 interpolation

Calculate the five Chebyshev nodes in the interval [-1,1] which are used when interpolating with a degree four polynomial. Evaluate the function f(x)=2arcsin(x) at each of these points. Construct the degree four Chebyshev polynomial. Evaluate the resulting polynomial at x=0.8 and compare with the actual value of the function.

A nationwide test taken by high school sophomores

A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of to . In a recent year, the national mean score for the writing section was , with a standard deviation of . Based on this information, complete the following statements about the distribution of the scores on the writi

Finding lower and upper limits based on a known distribution

Please show me how to do these problems correctly. A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 49.6, with a standard deviation of 10.9. Based on this information, complete the followi

Chebyshev's Theorem,

A distribution has a mean of 260 and a standard deviation of 18. Using Chebyshev's Theorem, what is the percentage of data values that will fall in the range of 215 to 305?