Answered: In the game of roulette, a wheel…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter3: Solving Equation And Problems

Section3.6: Problem Solving: Using Charts

Problem 2OE

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In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1. Complete parts (a) through (g) below.

Click here to view the standard normal distribution table (page 1).

Click here to view the standard normal distribution table (page 2).

(a) Construct a probability distribution for the random variable X, the winnings of each spin.

x	P(x)
35	0.02630.0263
−1	0.97370.9737

(Type integers or decimals rounded to four decimal places as needed.)

(b) Determine the mean and standard deviation of the random variable X. Round your results to the nearest penny.

μ=negative 0.05−0.05

σ=5.765.76

100

times so that

n=100.

Describe the sampling distribution of

the mean amount won per game.

The sample mean

approximately normal.

What are the mean and standard deviation of the sampling distribution of

Round your results to the nearest penny.

μx=negative 0.05−0.05

σx=0.580.58

(d) What is the probability of being ahead after playing the game

100

times? That is, what is the probability that the sample mean is greater than 0 for

n=100?

P(x>0)=0.46360.4636

(Type an integer or decimal rounded to four decimal places as needed.)

(e) What is the probability of being ahead after playing the game

300

times?

P(x>0)=0.43720.4372

(Type an integer or decimal rounded to four decimal places as needed.)

(f) What is the probability of being ahead after playing the game

1000

times?

P(x>0)=0.38640.3864

(Type an integer or decimal rounded to four decimal places as needed.)

(g) Compare the results of parts (d) through (f). What lesson does this teach you?

The probability of being ahead increases as the number of games played increases.

The probability of being ahead decreases as the number of games played decreases.

The probability of being ahead decreases as the number of games played increases.

Your answer is correct.

The probability of being ahead remains the same as the number of games played varies.

Question is complete. Tap on the red indicators to see incorrect answers.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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