A pollster wishes to obtain information on intended voting behavior in a two party system and samples a fixed number (n) of voters. Let X_1 ..., X_n denote the sequence of independent Bernoulli random variables representing voting intention, where E(X_l) = p, i = 1, ..., n (a) Suppose the number of voters n is fixed, compute
1. A manufacturing intraocular lens is in a process of verifying a polishing machine. The polisher will be accepted only if the percentage of polished lenses containing surface defects does not exceed 1.5%.They took a sample of 300 lenses and found 5 lenses that had surface defect. Formulate a test appropriate for verification o
Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Discuss the purpose of using such a visual in working out probability.
The president of a large oil company must decide how to invest the company's $10 million of excess profit. He could invest the entire sum in solar energy research, or he could use the money to research better ways of processing coal so that it will burn more cleanly. His only other option is to put half of this R&D money into so
Problem 1. Use the following data set. The data set represents incomes (in thousands of dollars) of 20 employees at an engineering firm. 50, 48, 46, 59, 44, 43, 35, 59, 48, 53, 46, 59, 52, 48, 51, 59, 53, 51, 53, 52 (a) Find the range, mean, median, and mode of the data set. (b) Make a frequency distribution for the data se
Suppose someone gives you 9 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $9.00 if you succeed and you lose $2.00 if you fail. What is the expected value of this game to you? Should you expect to win or loose the expected value in the first game? What can you expect if you pla
Use the theoretical method to determine the probability of the given outcome or event. A bag contains 5 red candies, 15 blue candies, and 20 yellow candies. What is the probability of drawing a red candy? a blue candy? A yellow candy? Something besides a yellow candy? The probability of drawing a red candy is ______ (round t
A magazine ran a sweepstakes in which prices were (see list below). listed along with the chance of winning. values 1 chance out of $1,000,000 ; 80,000,000 $100,000 ; 120,000,000
We repeatedly throw a die, stopping when the value of the throw exceeds the value of the first throw. Compute the expectation value of the number of throws.
Examples of the binomial and Poisson distributions are all around us. - Identify a real-life example or application of either the binomial or poisson distribution. - Specify how the conditions for that distribution are met. - Suggest reasonable values for n and p (binomial) or mu (poisson) for your example. -
Q1: A sample of n independent observations x1, x2, . . . , xn are obtained of a random variable having a Poisson distribution with mean ?. Show that the maximum likelihood estimate of ? is the sample mean [see the attached file]. Show that corresponding estimator (X) is an unbiased estimator of ?, and has variance ?/n.
Assume that the average number of traffic accidents requiring medical assistance between 7 and 8 AM on Wednesday mornings is 1. What then is the chance that there will be a need for exactly 2 ambulances during that time slot on any given Wednesday morning?
Hi, I need some assistance with the following two questions. I am not sure that I understand the questions fully. Any assistance would be appreciated. 1. What are some conditions under which business decisions are made using probability concepts? Provide at least two examples of subjective probability. 2. What are the chara
Assume that the Wheel of Fortune has 24 slots, each subtending 15 degrees. There are two bankrupt slots. 1. Assuming each spin has a random result, what are the odds of hitting a bankrupt slot? 2. a) Does the layout of bankrupt slots impact this result? b) Explain your answer.
Diffusion as a probability for a random walk - please see the attached question. No big derivation is required and this may be able to be answered in just a few lines. The main point is to show the probability of hopping using only the values given at the bottom of the attached pdf.
There are 8 spoiled apples in a container of 27 apples set for inspection. A sample is drawn, for 4 apples at random, from the container during inspection. a) How many ways can the 4 apples be drawn in which there are 1 good apple and 3 spoiled apples? b) How many ways can the 4 apples be drawn in which none are spoiled? c)
A company that has 327 employees chooses a committee of 17 to represent employee retirement issues. When the committee was formed, none of the 83 minority employees were selected. 1. Find the number of ways 17 employees can be chosen from 327. 2. Find the number of ways 17 employees can be chosen from 244 non-minorities. 3. I
1. Are the events mutually exclusive (Yes or No)? Event A: Randomly select a person between 18 and 24 years old. Event B: Randomly select a person that drives a convertible. 2. Decide if the events are mutually exclusive. Event A: Randomly select a person who uses email. Event B: Randomly select a person that uses social
You are given 9 to 1 odds at tossing 3 heads in a row with three coins; meaning you win $9 if you succeed and lose $1 if you fail. a) Find the expected value (to you) of the game. b) If you play one game would you expect to win or lose the game? Explain. c) What about if you play 100 games?
Use the empirical method to estimate the probability. You count 42 heads when you toss a coin 100 times. If you don't know whether the coin is fair what is the probability the next toss will be a tail?
A standard deck of 52 cards is shuffled (all possible orderings are equally likely) and the cards are turned up one at a time. What is the probability that all the aces will appear before any of the tens?
You give $3 for a bet in a casino game and there is a 253/495 probability that you will lose your $3 and there is a 242/495 probability that you will make a net gain of $3 (If you win the casino gives you $3 and you keep your $3 bet so the net gain is $3). 1. What is your expected value? 2. In the long run how much do you
Use the at least once rule to find the probability of the following event. Drawing at least one black card when you draw a card from a standard deck 6 times, replacing the card each time you draw so that there are always 52 cards in the deck.
Length of metal strips produced by a machine are normally distributed with mean length of 150 cm and a standard deviation of 10 cm. Find the probability that the length of a randomly selected strip is: (a) Shorter than 165 cm. (b) Longer than 170 cm. (c) Between 145 cm and 155 cm.
Let P(A) denote the probability of a set A, and let A / B and A / B denote the union and intersection, respectively, of two sets A and B. If P(A) = 0.7, P(B) = 0.6, P(C) = 0.3, and P(A / C) = 0.2, find the minimum and maximum possible values of P(A / (B / C)).
1. True or False? 1.08 is a valid value for the correlation coefficient, r. 2. True or False? -0.835 is a valid value for the correlation coefficient, r. 3. Using the scatter plot below, determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables.
Suppose that next year the U.S. will be in one of the following economic conditions: Boom, Moderate Growth, Recession, or Depression. The probability that each economic condition will occur, and that a jewelry store will earn profits within that broader economic condition are listed below: Economic Condition Probability Jewel
The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of . = 3 per day (approximately Poisson in nature). The crew can service an average of µ = 8 machines per day, with a repair time distribution that resembles the exponential distribution. Please help me with the
On a Jukebox with 2000 songs, what is the probability that a single song will play during a 1 hour period, a 3 hour period, a 5 hour period, or a 12 hour period? How many times would a single song play during the periods described?
A box contains two defective Christmas tree lights that have been inadvertently mixed with eight non-defective lights. If the lights are selected one at a time without replacement and tested until both defective lights are found, what is the probability that both defective lights will be found after exactly three trials?