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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.

- 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?

**a.**

To determine

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

**Calculation:**

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

Event

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

The total frequency is 944 and frequency of the event

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

Thus,

Similarly other probabilities are obtained as shown in the table:

Experimental Outcome | Age Financially Independent | Number of Responses | Probability |

16 to 20 | 191 |

**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.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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