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Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to 18 and asked at what age they think that they will become financially independent ( USA Today , April 30, 2012). The responses of 944 teenagers who answered this survey question are as follows. Age Financially Independent Number of Responses 16 to 20 191 21 to 24 467 25 to 27 244 28 or older 42 Consider the experiment of randomly selecting a teenager from the population of teenagers aged 14 to 18. a. Compute the probability of being financially independent for each of the four age categories. b. What is the probability of being financially independent before the age of 25? c. What is the probability of being financially independent after the age of 24? d. Do the probabilities suggest that the teenagers may be somewhat unrealistic in their expectations about when they will become financially independent?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 4.2, Problem 20E
Textbook Problem
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Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to 18 and asked at what age they think that they will become financially independent (USA Today, April 30, 2012). The responses of 944 teenagers who answered this survey question are as follows.

Age  Financially Independent Number of Responses
16 to 20 191
21 to 24 467
25 to 27 244
28 or older 42

Consider the experiment of randomly selecting a teenager from the population of teenagers aged 14 to 18.

  1. a. Compute the probability of being financially independent for each of the four age categories.
  2. b. What is the probability of being financially independent before the age of 25?
  3. c. What is the probability of being financially independent after the age of 24?
  4. d. Do the probabilities suggest that the teenagers may be somewhat unrealistic in their expectations about when they will become financially independent?

a.

To determine

Compute the probability of being financially independent for each of the four age categories.

Explanation of Solution

Calculation:

The table provide information about different ages where teenagers are financially independent and corresponding frequencies.

Event E1 denotes that age group 16 to 20.

The probability of the event can be obtained as shown below:

P(E)=Number of ways event occursTotal frequency

The total frequency is 944 and frequency of the event E1 is 191. Substitute these value in the above equation.

The probability of the event can be obtained as shown below:

P(E1)=191944=0.2023

Thus, P(E1)=0.2023.

Similarly other probabilities are obtained as shown in the table:

Experimental OutcomeAge Financially IndependentNumber of ResponsesProbability
E116 to 20191191944=0

b.

To determine

Compute the probability of being financially independent before the age of 25.

c.

To determine

Compute the probability of being financially independent after the age of 24.

d.

To determine

Check whether the probabilities suggest that teenagers may be somewhat unrealistic in their expectation about when they will become financially independent.

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