Question

Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to 18 and asked at what age they think they will become financially independent. The responses of 944 teenagers who answered this survey question as follows:

Age Financially Independent Number of Responses
16 to 20 151
21 to 24 487
25 to 27 244
28 or older 62

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

Required:
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?

Answer 1

(a) Shown below

(b) 0.68

(c) 0.32

Explanation:

The frequency distribution is:

Age Group Financially Independent Number of Responses

16 to 20 151

21 to 24 487

25 to 27 244

28 or older 62

Total 944

(a)

Compute the probability of being financially independent for each of the four age categories as follows:

`P(\text{16 to 20})=(151)/(944)=0.159958\approx 0.16\\\\P(\text{21 to 24})=(487)/(944)=0.515890\approx 0.52\\\\P(\text{25 to 27})=(244)/(944)=0.258475\approx 0.26\\\\P(\text{28 or older})=(62)/(944)=0.065678\approx 0.06`

(b)

Compute the probability of being financially independent before the age of 25 as follows:

P (Financially Independent before 25) = P (16 to 20) + P (21 to 24)

= 0.16 + 0.52

= 0.68

Thus, the probability of being financially independent before the age of 25 is 0.68

(c)

Compute the probability of being financially independent after the age of 24 as follows:

P (Financially Independent after 24) = P (25 to 27) + P (28 or older)

= 0.26 + 0.06

= 0.32

Thus, the probability of being financially independent after the age of 24 is 0.32.