Chapter 5: Q14 (page 197)

In Exercises 7–14, determine whether a probability
distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
When betting on the pass line in the dice game of craps at the Mohegan Sun casino in Connecticut, the table lists the probabilities for the number of bets that must be placed in order to have a win.
x
P(x)
1
0.493
2
0.25
3
0.127
4
0.064

Expert verified

The requirement for the sum of probabilities to be equal to 1 is not satisfied.

Step by step solution

The probability distribution for the number of bets that must be placed to win is provided.

Let x represent the number of bets that must be placed to win.

The requirements are as follows:

1)The variable x is anumerical random variable.

2)The sum of the probabilities is computed as:

$\sum P (x) = 0.493 + 0.25 + 0.127 + 0.064 = 0.934$

Therefore,the sum of the probabilities is not equal to 1.

3) Each value of P(x) is between 0 and 1.

Thus, the requirement for the sum of probabilities to be equal to 1 is not satisfied.

Therefore, the mean and standard deviation cannot be computed.

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