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Question

The television game show Deal or No Deal begins with indidvidual suitcase containing the amounts of 1 cent, $1, $5, $10, $25, $50, $75, $100, $200, $300, $400, $500, $750, $1000, $5000, $10,000 $25,000 $50,000 $75,000 $100,000 $200,000 $300,000 $400,000 $500,000 $750,000 and $1,000,000. 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 $750,000 or $1,000,000 unsually high? Why or Why not

Answer 1

Step 1:

(a)

The deal and No deal television game has individual suitcase containing amounts are

1 cent, $ 1, $5, $10, $25, $50, $75, $100, $200, $300, $400, $500, $750, $1000, $5000, $10,000 $25,000 $50,000 $75,000 $100,000 $200,000 $300,000 $400,000 $500,000 $750,000 and $1,000,000.

Number of suitcase is 26.

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 each outcome is .

Expected value:

Expected value of the strategy is 131477.53.

Solution:

Expected value of the strategy is 131477.53.

Answer 2

Step 1:

(b)

Find the standard deviation.

First find

Standard deviation :

Standard deviation is 253584.47.

Solution:

Standard deviation is 253584.47.

Answer 3

Step 1:

(c)

Range Rule of Thumb:

Maximum usual value =  .

Maximum usual value is 638646.4743

Minimum usual value = .

Minimum usual value is truncated to 0.

Minimum usual value is 0.

The range of values for usual number of suitcase containing amount lies between 0 to 638646.4743.

Solution:

The range of values for usual number of suitcase containing amount lies between 0 to 638646.4743.

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 suitcase containing amount lies between 0 to 638646.4743.

The result $750,000 and $1,000,000 are out of the range.

So they are considered as unusual.

$750,000 and $1,000,000 are unusual outcomes.

Solution:

$750,000 and $1,000,000 are unusual outcomes.