Step 1:

(a)

The arcade version of television show deal and No deal has individual suitcase containing amounts

2 tickets, 4 tickets, 6 tickets, 8 tickets, 10 tickets, 12 tickets, 14 tickets, 16 tickets, 20 tickets, 24 tickets, 30 tickets, 40 tickets, 50 tickets, 60 tickets, 100 tickets and 250 tickets.

Number of suitcase is 16.

Expected value:

The expected value of a discrete random variable is denoted by E, and it represents the mean value of the outcomes.

It is obtained by finding the value of , where is the probability of each outcome.

Probability of choosing no deal is .

Expected value:

Expected value of the strategy is 40.375.

Solution:

Expected value of the strategy is 40.375.

Step 1:

(b)

Find the standard deviation.

First find

Standard deviation :

Standard deviation is 59.5869.

Solution:

Standard deviation is 59.5869.

Step 1:

(c)

Range Rule of Thumb:

Maximum usual value =  .

Maximum usual value is 159.5488.

Minimum usual value = .

Minimum usual value is truncated to 0.       (since amount cannot be negative)

Minimum usual value is 0.

The range of values for usual number of suitcase containing amount lies between 0 to 159.5488.

Solution:

The range of values for usual number of suitcase containing amount lies between  0 to 159.5488.

Step 1:

(d)

The values considered under the range are usual outcomes otherwise they are unusual outcomes.

The range of values for usual number of suitcase containing amount lies between 0 to 159.5488.

The two results are 100 tickets or 250 tickets.

The result of 100 tickets is in the range 0 to 159.5488.

The result of 100 tickets is considered usual outcome.

The result of 250 tickets is out of the range 0 to 159.5488.

The result of 250 tickets is considered unusual outcome.

Solution:

The result of 100 tickets is usual outcome.

The result of 250 tickets is unusual outcome.