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Question

The arcade verision of television game show Deal or No Deal begins with indidvidual suitcase containing the amounts of 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 If a player adopts the strategy of choosing the option of "no deal" until one suitcase remains, the payoff is one of the amounts listed, and they are all equally likely.

A. FInd the expected value for this strategy.

B. Find the value of the standard deviation.

C. Use the range rule of thumb to identify the range of usual outcomes.

D. Based on the preceding results, is a result of 100 tickets or 250 tickets unsually high? Why or Why not

Answer 1

Step 1:

(a)

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

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 containing tickets are 16.

Find the 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.

Answer 2

Step 1:

(b)

Find the standard deviation.

First find .

Standard deviation :

Standard deviation is 59.5869.

Solution:

Standard deviation is 59.5869.

Answer 3

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.

Minimum usual value is 0.

The range of values for usual number of outcome lies between 0 to 159.5488.

Solution:

The range of values for usual number of outcome lies between  0 to 159.5488.

Answer 4

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 outcome 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 as usual outcome.

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

The result of 250 tickets is considered as unusual outcome.

Solution:

The result of 100 tickets is usual outcome.

The result of 250 tickets is unusual outcome.