Consider a population of 3000 people, 1400 of whom are men. Assume that 700 of the women in this population earn at least $60,000 per year, and 500 of the men earn less than $60,000 per year. a. What is the probability that a randomly selected person from this population earns less than $60,000 per year? b. If a randomly selected person is observed to earn less than $60,000 per year, what is the probability that this person is a man? c. If a randomly selected person is observed to earn at least $60,000 per year, what is the probability that this person is a woman?

The second law of thermodynamic, according to Clausius statement says Select one: a. it is impossible to construct a device than can transfer heat from a hotter body to a cooler body without any effect b. it is possible to construct a device that can transfer heat from a hotter body to another hooter body without any effect c. it is possible to construct a device than can transfer heat from a cooler body to a hotter body without any effect d. it is impossible to construct a device than can transfer heat from a cooler body to a hotter body without any effect.

2. A daily demand for loaves of bread at a grocery store is given by the following probability distribution: 100 150 0.20 0.25 200 0.30 250 0.15 300 0.10 p(x) and the cost payoff matrix (in Rs) as: Daily Demand 100 150 200 250 350 100 300 300 300 300 300 150 250 450 450 450 450 200 200 400 600 600 600 250 150 350 550 750 750 350 100 300 500 700 900 i) Determine the best daily stock of loaves of bread using the expected monetary value (EMV) criterion. ii) Determine the best daily stock of loaves of bread using the expected opportunity loss (EOL) criterion. i) How much will the decision maker spend to get additional information? Daily Stock

A gambler in Las Vegas is cutting a deck of cards for $1,000. What is the probability that the card for the gambler will be the following? a. A face card b. A queen c. A spade d. A jack of spades

|At the Pleasant Haven Hotel there are 36 rooms. The profit earned when a room is sold for a night is $53. If Pleasant Haven overbooks, by selling more reservaitions than they have rooms and they end up having a customer whose reservation cannot be fulfilled, the loss to Pleasant Haven is $30 for that customer. Regardless of the number of rooms booked, the probability of one no show is 60% and the probability of 2 no shows is 20%. There is zero probability of more than 2 no shows. For a night when requests are exceeding the 36 rooms, what is the optimal number of reservations to accept? Assume there is no penalty for a customer who does not show up, i.e., Pleasant Haven does not make $53 on a customer that is a no show. What is the expected net for booking each of the following: (Net means profit minus any overbooking loss.) 36 customers 37 customers 38 customers What is the best number of book?

An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 25 percent. If the binomial probability distribution is applicable, then the probability that there will be at least four claims during the year is equal to A- 0.716 B- 0.370 C- 0.595 D- 0.552

A polling firm is taking a survey regarding a proposed new law. Of the voters polled, 30% are in favor of the law. If 10 people are surveyed, what is the probability that 4 will indicate that they are opposed to the passage of the new law?

For a normal distribution, a positive value of Z indicates that

Suppose you sample one value from a uniform distribution with a = 0 and b=20. a. What is the probability that the value will be between 12 and 172 b. What is the probability that the value will be between 4 and 72 c. What is the mean? d. What is the standard deviation? a. The probability that the value will be between 12 and 17 is (Type an integer or a decimal)

A chemical company is trying to decide whether to build a pilot plant now for a new chemical process or to build the full plant now. If it builds a pilot plant now, it could expand later to a full plant or license the plant to another company. It would cost $2 million to build the pilot plant and another $2 million later to expand it. If the company builds the full plant now, it would cost $3.5 million to construct.The returns the company expects to get from the full production plant depend on the market. There is a 60% chance the market will be robust, a 30% chance it will remain stable, and a 10% chance it will become stagnate. The returns are estimated to be $5 million if it is robust, $3 million if it is stable, and $1 million if it is stagnate.Before the company expands the pilot plant, it plans to conduct a comprehensive study. Based on past experience, it expects the study to report a 60% chance of favorable outcome for expansion and a 40% unfavorable chance. In either case, it…