A S1 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 1. $500 0.001 Payoff X Probability 0.999 Each day's drawing is independent of other drawings. You must show your work in answering the following questions What are the mean and standard deviation of X? a. b. Joe buys a Pick 3 ticket twice a week. What does the law of large numbers say about the average payoff Joe receives from his bets? What does the central limit the orem say about the distribution of Joe's average payoff after 104 bets in a year? c. Joe comes out ahead for the year if his average payoff is greater than $1(the amount he spent each day on a ticket). What is the probability that Joe ends the year head? d.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Please help me with question 1D. thank you

A S1 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
1.
$500
0.001
Payoff X
Probability
0.999
Each day's drawing is independent of other drawings. You must show your work in answering
the following questions
What are the mean and standard deviation of X?
a.
b. Joe buys a Pick 3 ticket twice a week. What does the law of large numbers say about the average
payoff Joe receives from his bets?
What does the central limit the orem say about the distribution of Joe's average payoff after 104
bets in a year?
c.
Joe comes out ahead for the year if his average payoff is greater than $1(the amount he spent each
day on a ticket). What is the probability that Joe ends the year head?
d.
Transcribed Image Text:A S1 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 1. $500 0.001 Payoff X Probability 0.999 Each day's drawing is independent of other drawings. You must show your work in answering the following questions What are the mean and standard deviation of X? a. b. Joe buys a Pick 3 ticket twice a week. What does the law of large numbers say about the average payoff Joe receives from his bets? What does the central limit the orem say about the distribution of Joe's average payoff after 104 bets in a year? c. Joe comes out ahead for the year if his average payoff is greater than $1(the amount he spent each day on a ticket). What is the probability that Joe ends the year head? d.
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