Question

A game is played. One dollar is bet and 3 dice are rolled. If the sum...

A game is played. One dollar is bet and 3 dice are rolled. If the sum of the eyes of the dice is smaller than 5, one wins 20 dollar otherwise one looses the 1 dollar.

Find the approximation of the distribution of the total wins after 200 games. What is the Probabilty that the total win is positive. Use the CLT and state why.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

P( eyes of the dice is smaller than 5)=4/216=1/54

hence

x P(x) xP(x) x2P(x)
20    1/54 0.370 7.407
-1 53/54 -0.981 0.981
total -0.611 8.389
E(x) =μ= ΣxP(x) = -0.6111
E(x2) = Σx2P(x) = 8.3889
Var(x)=σ2 = E(x2)-(E(x))2= 8.015
std deviation=         σ= √σ2 = 2.8312

hence expected win after 200 games = 200*(-0.6111)=-122.22

and standard deviation =2.8312*sqrt(200)=40.0386

as sample size is greater then 30 ; therefore we can use normal approximation

therfore from normal approximation: P( that the total win is positive )=P(X>0)=P(Z>(0-(-122.22))/40.0386)=P(Z>3.05)

=0.0011

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
. A dice game is played as follows: you pay one dollar to play, then you...
. A dice game is played as follows: you pay one dollar to play, then you roll a fair six-sided die. If you roll a six, you win three dollars. Someone claims to have won a thousand dollars playing this game nine thousand times. How unlikely is this? Find an upper bound for the probability that a person playing this game will win at least a thousand dollars.
A gambler plays a dice game where a pair of fair dice are rolled one time...
A gambler plays a dice game where a pair of fair dice are rolled one time and the sum is recorded. The gambler will continue to place $2 bets that the sum is 6, 7, 8, or 9 until she has won 7 of these bets. That is, each time the dice are rolled, she wins $2 if the sum is 6, 7, 8, or 9 and she loses $2 each time the sum is not 6, 7, 8, or...
In a game of “Chuck a luck” a player bets on one of the numbers 1...
In a game of “Chuck a luck” a player bets on one of the numbers 1 to 6. Three dice are then rolled and if the number bet by the player appears i times (where i equals to 1, 2 or 3) the player then wins i units. On the other hand if the number bet by the player does not appear on any of the dice the player loses 1 unit. If x is the players’ winnings in the...
A lottery payoff. A $1 bet in a state lottery's Pick 3 game pays $500 if...
A lottery payoff. A $1 bet in a state lottery's Pick 3 game pays $500 if the three-digit number you choose exactly matches the winning number, which is drawn at random. Here is the distribution of the payoff X: Payoff $0; probability: 0.999. Payoff $500; Probability: 0.001. Each day's drawing is independent of other drawings. (a) Hoe buys a Pick 3 ticket twice a week. The number of times he wins follows a B(104, 0.001) distribution. Using the Poisson approximation...
Joe Smith plays a betting game with his friends. He puts in one dollar to join...
Joe Smith plays a betting game with his friends. He puts in one dollar to join the game. If he wins the game, he gets $2. If he loses, he gets nothing, so his gain is –$1. Joe Smith is planning to play the game 100 times. The 100 outcomes will be independent of one another. Let Vi, i = 1, 2, ..., 100 be the 100 outcomes. Then each Vi has the same probability distribution: v -1 1 p(v)...
JAVA: MUST BE DONE IN JAVA Assignment: Write algorithms and programs to play “non-betting” Craps. Craps...
JAVA: MUST BE DONE IN JAVA Assignment: Write algorithms and programs to play “non-betting” Craps. Craps is a game played with a pair of dice. In the game, the shooter (the player with the dice) rolls a pair of dice and the number of spots showing on the two upward faces are added up. If the opening roll (called the “coming out” roll) is a 7 (“natural”) or 11 (“yo-leven”), the shooter immediately wins the game. If the coming out...
After losing his blackjack game, Ebert then goes to the race track. He wants to bet...
After losing his blackjack game, Ebert then goes to the race track. He wants to bet $20 on one of the following horses: Horse name Odds Against Maximum 8:1 Improbable 5:1 Code of Honor 12:1 Game Winner 9:2 Tax 20.1 A)Using the odds given, calculate the probability of each horse winning the race. B)Based on your calculation in part (a), which horse should ebert bet on? Why? C) at a horse race, if the odds against your horse are a:b...
In java create a dice game called sequences also known as straight shooter. Each player in...
In java create a dice game called sequences also known as straight shooter. Each player in turn rolls SIX dice and scores points for any sequence of CONSECUTIVE numbers thrown beginning with 1. In the event of two or more of the same number being rolled only one counts. However, a throw that contains three 1's cancels out player's score and they mst start from 0. A total of scores is kept and the first player to reach 100 points,...
MATHEMATICS 1. The measure of location which is the most likely to be influenced by extreme...
MATHEMATICS 1. The measure of location which is the most likely to be influenced by extreme values in the data set is the a. range b. median c. mode d. mean 2. If two events are independent, then a. they must be mutually exclusive b. the sum of their probabilities must be equal to one c. their intersection must be zero d. None of these alternatives is correct. any value between 0 to 1 3. Two events, A and B,...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary rivals? How will the acquisition of Reebok by Adidas impact the structure of the athletic shoe industry? Is this likely to be favorable or unfavorable for New Balance? 2- What issues does New Balance management need to address? 3-What recommendations would you make to New Balance Management? What does New Balance need to do to continue to be successful? Should management continue to invest...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT