The weekly wages of steel workers at a steel plant are normally distributed with a mean weekly wage of $940 and a standard deviation of $85. There are 1540 steel workers at this plant. a) What is the probability that a randomly selected steel worker has a weekly wage i) Of more than $850? ii) Between $910 and $960? b) What percentage of steel workers have a weekly wage of at most $820? c) Determine the total number of steel workers with a weekly wage within one standard deviation of the mean. d) Find the lowest and highest weekly wages for the middle 70% of the wage scale.

Two teams, the Exponents and the Radicals, square off in a best of 5 math hockey tournament. Once a team wins 3 games, the tournament is over.

The schedule of the tournament (for home games) goes: E-R-E-R-E

If the Exponents are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is a 45% chance they'll win.

Find the probability that the Exponents win the series. Round answers to at least 4 decimal places.

Consider a game where each of 10 people randomly drop a dollar bill with their name on it into a bag and then take turns picking a dollar each from the bag.

a) What is the probability that at least one person picks a bill with his name on it?

b) Given that the first person to pick a bill with his name on it wins all the money, what are the chances of winning if you draw first? What is the best order to draw to increase your chances of winning?

Two players A and B play a dice game with a 6-face fair dice. Player A is only allowed to roll the dice once. Player B is allowed to roll the dice maximally twice (that is, Player B can decide whether or not she or he would roll the dice again after seeing the value of the first roll). If the player with the larger final value of the dice wins, what is the maximal probability for Player B to win the game?

1mol of an ideal gas is inside a cylinder with a piston under a pressure of 6 atm. When reducing the pressure to 2 atm at constant T = 300K:
(a) Who is doing work, the piston or the gas?
(b) What is the type of process for the maximum work? Find the maximum amount of work.
(c) What is the type of process for the minimum work? Find the minimum amount of work.

2. Every day, Chung-Li buys a scratch-off lottery ticket with a 40% chance of winning some prize. He noticed that whenever he wears his red shirt he usually wins. He decided to keep track of his winnings while wearing the shirt and found that he won 6 out of 9 times.

• Let's test the null hypothesis that Chung-Li's chance of winning while wearing the shirt is 40% as always versus the alternative that the chance is somehow greater.
• The table at right sums up the results of 1000 simulations, each simulating 9 lotteries with a 40%, percent chance of winning.
• According to the simulations, what is the probability of winning 6 times or more out of 9?
• 74/1000 = .00074
• Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis.
• What should we conclude regarding the hypothesis?
  • We cannot reject the null hypothesis.
  • We should reject the null hypothesis.

----------USING JAVA-----------

Your objective is to beat the dealer's hand without going over 21.

• Cards dealt (randomly) are between 1 and 11.
• You receive 2 cards, are shown the total, and then are asked (in a loop) whether you want another card.
• You can request as many cards as you like, one at a time, but don't go over 21. (If you go over 21 it should not allow you any more cards and you lose)
• Determine the dealer's hand by generating a random number between 1 and 11 and adding 10 to it.
• Compare your hand with the dealer's hand and indicate who wins (dealer wins a draw)

Thank you!

In Java please!!

Your objective is to beat the dealer's hand without going over 21. Cards dealt (randomly) are between 1 and 11. You receive 2 cards, are shown the total, and then are asked (in a loop) whether you want another card. You can request as many cards as you like, one at a time, but don't go over 21. (If you go over 21 it should not allow you any more cards and you lose) Determine the dealer's hand by generating a random number between 1 and 11 and adding 10 to it. Compare your hand with the dealer's hand and indicate who wins (dealer wins a draw)

Write a Python program to simulate a very simple game of 21
•Greet the user.
•Deal the user a card and display the card with an appropriate message.
•Deal the user another card and display the card
.•Ask the user if they would like a third card. If so, deal them another card and display the value with an appropriate message.
•Generate a random number between 10 and 21 representing the dealer’s hand. Display this value with an appropriate message.
•If the user’s total is greater than the dealer’s hand and the user’s total is NOT greater than 21, the user wins, otherwise the dealer wins. Display the player’s and the dealer’s totals along with an appropriate message indicating who won.

Let A and B be two stations attempting to transmit on an Ethernet. Each has a steady queue of frames ready to send; A’s frames will be numbered ?1, ?2 and so on, and B’s similarly. Let ? = 51.2 ???? be the exponential backoff base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times of 0 × ? and 1 × ?, respectively. As a result, Station A transmits ?1 while Station B waits. At the end of this transmission, B will attempt to retransmit ?1 while A will attempt to transmit ?2. These first attempts will collide, but now A backs off for either 0 × ? or 1 × ? (with equal probability), while B backs off for time equal to one of 0 × ?, 1 × ?, 2 × ? and 3× ? (with equal probability).

What is the probability that A wins all the ? backoff races. (? is a given constant)