Probability of fewer than 2 chickens being contaminated

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have less than 2 contaminated chickens? Round to 3 decimal places.

Probability of an oblique impact

The solar system as it exists today has been shaped by large impacts that happened during the formation of the planets. Some of those impacts have been argued to have been oblique impacts. An example is the impact that formed the Imbrium basin on the Moon: https://news.brown.edu/articles/2016/07/...

Bayesian inference problem involving Poisson statistics

In a laboratory a set of samples of radioactive materials is kept. Half of the samples consists of N atoms with a half life of t1, and the other half consists of N atoms with a half life of t2. A sample is drawn randomly from the entire set, during a time interval of T, no decays are detected. Compu...

Expectation value of the maximum of two variables

Consider n variables drawn independently from an arbitrary probability distribution. We derive the general expression of the probability density for the kth largest variable. Derive the general expression for the expectation value of the largest variable. Evaluate this expectation value for the sta...

Calculus and Probability

Please see the attachment for the full questions. The graph of a function f: [-2, p] -> R is shown below. The average value of f over the interval [-2, p] is zero. The area of the shaded region is 25/8. If the graph is a straight line, for 0 <= x <= p, then the value of p is: a. 2 b. 5 c....

Find the probability using Bayes' Theorem

Assume breast cancer affects .006 of the female population between 45 and 55 years of age. There are two kinds of positive test results: * True Positive (the test indicates you have a disease, and you actually have it.) *False Positive (the test indicate you have a disease, but you actually do no...

Use Both Normal Approximation and Poisson Approximation

a. Expand the expression (a + b) as a sum of terms in a and b. b. Steel bolts are produced to a specified length. There is a probability of 5% that a bolt will fall outside of this range. A sample of 7 bolts is extracted and measured. Assuming the bolt lengths are normally distributed, use your...

Normal Distribution Word Problems

1. A certain brand of flood lamps has a lifetime that is normally distributed with a mean of 3,750 hours and a standard deviation of 300 hours. a) What is the probability that a lamp will last for more than 4,000 hours? b) What is the probability that a lamp will last less than 3,000 hours? ...

Linear Programming: Minimziation of cost

Problem 2 - Dog Breeder A large breeder of a particular type of dog wishes to determine the quantities of available types of dog food that he should stock so that he can be assured that his dogs meet their nutritional requirements, but at the least cost possible. He has decided that he can do th...

Some questions on normal distribution

(NOTES) calculate the z-value using the appropriate formula z=x−μ σ z=x−μ σ and find the area under the curve for z-value. Normal distribution is calculated by subtracting upper limit area from lower limit area (Round all answers to three decimal places) The mean gas mileage for a h...

BP has three potential sites where it can build a drilling rig

BP has three potential sites where it can build a drilling rig. Due to its past experience, the CEO has instructed his management team to choose no more than one site. The costs, the revenues and the estimated outcomes for each site are given in the table below. Probabilities for the different out...

Accuracy of Genetic Test using technique of contingency table

Acme Manufacturing Company requires all of its 5000 employees to take a drug test. Suppose 2% of the employees actually use drugs (although the company does not know this number). The drug test is 95% accurate. 1.How many of Acme's employees use drugs?. 2.How many of the employees who use drugs g...

Statistics: Frequency Distributions

I have two questions. Please use Microsoft word to write out solution. 1) The scores in Mathematics of 15 students are given below. Find range, sample variance and standard deviation. 93 85 78 79 97 90 82 61 53 63 94 69 84 67 95 Show and explain your steps. 2) The following are...

math 540

Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the av...

Probability, Counting and Combination

See the attachment. 1) When dealing with probability using a dice, let's assume we have a two fair, 6-sided dice that are rolled together. a) What is the probability of the sum of the numbers on the dices to be 8 or larger? b) What is the probability of rolling a 12 on the dices? c) I...

Statistics: Replacement and Probability

See the attachment. 6. A coin and a die are tossed. What is the probability of getting a head on the coin and a 4 on the die? Franco has a bag with four letter tiles in it. All of the tiles are the same size and shape, as shown below.(see attachment). One face of each tile has a letter on it, ...

Probability of Type II Error and the Error of Margin

1. Consider the following test of whether the coin is fair. Toss a coin three times, if the coin lands whether all heads or tails, reject the Ho: p=1/2. If P=4/5, What is the probability of type II error for this procedure? 2. A sample of 350 orders for takeout at a local pizzeria found out th...

Compute the Mean and Standard Deviation of the Portfolio

An investor puts $15,000 in each of four stocks, labeled A, B, C, and D. The table below contains means and standard deviations of the annual returns of these 4 stocks. A: Mean = .15 Standard Deviation = .05 B: Mean = .18 Standard Deviation = .07 C: Mean = .14 Standard Deviation = .03 D: Me...

Compute the probability under the normal distribution

Given: 1) Invest $10,000 in Stock "ABC". 2) The daily returns are normally distributed with a mean of 0% and a standard deviation of 1%. Questions: 1) What is the probability that tomorrow's return on investment in ABC is exactly 0.9%? 2) Conditional on making a positive return tomorrow, what...

Probability: Possible Values

Q1. The function g: [-a,a] --> R, g(x) = sin(2(x-pi/6)) has an inverse function. The maximum possible value is a is:_____. Q2. Harry is a soccer player who practices penalty kicks many times each day. Each time Harry takes a penalty kick, the probability that he scores a goal is 0.7, independent...

Expected commission for a salesman

Based on past records, a salesman expects a $0 commission with probability 0.19, $1000 with probability 0.2, $2000 with probability 0.41 and $3000 or $4000 both with probability 0.1. Find the expected commission for the salesman.

Expected Value and Law of Large Numbers in Roulette

American roulette has 38 equally sized spaces two spaces are green and have numbers 0 and 00 on them and the rest numbered from 1 to 36. Half of the non-green spaces are red and half are black. The three-number bet, also a "row bet", is a bet on the three numbers in a vertical row on the roulett...

Mean and Variances, Estimates, Unbiased Property and Consistency

Please see the attachment for probability questions. Find the means and variances of these estimators. Hence answer the following questions, giving reasons for your answers. a) Which of these estimators are unbiased b) Which of the unbiased estimators is the most efficient as an estimator...

Maximum Likelihood Estimate & Fisher Information

A random sample of n observations is taken from a Poisson distribution with menu theta and the probability mass function attached. a) Write down the likelihood function b) Use the method of maximum likelihood to find the maximum likelihood estimator for theta. Confirm that you have located a maxi...

The Mean and Method of Moment Estimate of Uniform Distribution

Please see the attached file for probability questions. 1. Consider the probability density function for the uniform distribution on the range (a,b), b > a, fx (x) = (b - a)^-1, a < x < b. a) Sketch the probability density function fx (x). b) Derive the mean of the distribution in terms of...

Portfolio Risk Management, Systematic Risk & Unsystematic Risk

Suppose an individual investor starts with a portfolio that consists of one randomly selected stock. a. What will happen to the portfolio's risk if more and more randomly selected stocks are added? b. What are the implications for investors? Do portfolio effects have an impact on the way investo...

Probability Calculations: Bob's Umbrella

According to Bob, the payoffs of the several outcomes are as follows: a. If it is sunny and he is not carrying and umbrella, 10 b. If it is sunny and he is carrying an umbrella, 8 c. If it is rainy and he is not carrying an umbrella, 2 d. If it is rainy and he is carrying an umbrella, ...

Finding the Probability Density Function of a New Variable

1. The random variable X has mean u and variance sigma^2. The random variable Y is defined as Y=g(x). (a) Use a first order Taylor Series expansion about u to prove the following (see attachment). (b) If X follows the exponential distribution with mean u, so sigma^2 = u^2, and Y = g(x) = sqrt(...