Chapter 16, Problem 36E

(a)

To determine

To Explain: the reason for the large of standard deviation.

Explanation of Solution

There are data points that are scattered over a wide spectrum of the value that is the reason that standard deviation is high.

(b)

To determine

To find: the mean and standard deviation in benefit of the casino, if play five times.

Answer to Problem 36E

Mean = $0.40

Standard Deviation = $268.33

Explanation of Solution

Formula used:

  $E\left(X\right)={\displaystyle \sum xP\left(x\right)}$

  $SD\left(X\right)=\sqrt{\mathrm{var}\left(X\right)}$

Calculation:

The average casino 's benefit is when a person plays 5 times,

  $\begin{array}{c}E\left(x\right)=\left(1-\$0.92\right)\times 5\\ =\$0.40\end{array}$

When people play five times, the net profit of the casino is $0.40.

If it plays five times, the casino's standard performance deviation is

  $\begin{array}{c}S\left(x\right)=\sqrt{{120}^2\times 5}\\ =\$268.33\end{array}$

The standard deviation in the casino earnings when you play 5 times is $268.33.

(c)

To determine

To Find: the mean and standard deviation in casino benefit as players 1000 times a day use this machine.

Answer to Problem 36E

Mean = $80

Standard deviation = $3794.33

Explanation of Solution

Formula used:

  $E\left(X\right)={\displaystyle \sum xP\left(x\right)}$

  $SD\left(X\right)=\sqrt{\mathrm{var}\left(X\right)}$

Calculation:

If 1000 times a day a gambler plays the machine, the casino benefit mean is, $\begin{array}{c}E\left(x\right)=\left(1-\$0.92\right)\times 1000\\ =\$80\end{array}$

The casino benefit is $80 if a player runs the game 1000 times a day.

If a player operates the game 1000 times a day, the casino’s profit standard deviation is

  $\begin{array}{c}S\left(x\right)=\sqrt{{120}^2\times 1000}\\ =\$3794.33\end{array}$

The standard deviation from casino benefit is $3,794,33 if a player runs the game 1000 times a day.

(d)

To determine

To Explain: that it could be beneficial for the casino.

Explanation of Solution

The casino is estimated to be profitable compared to the overall slot earning jackpot playouts of $0.29. This makes the casino more profitable because of overall slot machines. $0.29.