Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to
ID: 3043595 • Letter: J
Question
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 ques tion are as follows 20. Number of Responses 191 467 244 42 Financially Independent 16 to 20 21 to 24 25 to 27 28 or older 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?Explanation / Answer
a. Total number of responses = 191+467+244+42 = 944
P [ financially independent between 16 to 20 ] = 191/944 = 0.2023305
P [ financially independent between 21 to 24 ] = 467/944 = 0.4947034
P [ financially independent between 25 to 27 ] = 244/944 = 0.2584746
P [ financially independent in 28 or older ] = 42/944 = 0.04449153
b. P [ financially independent before age 25 ] = P [ financially independent between 16 to 20 ] + P [ financially independent between 21 to 24 ] = 0.2023305+ 0.4947034 = 0.6970339
c. P [ financially independent after age 24 ] = P [ financially independent between 25 to 27 ]+P [ financially independent in 28 or older ] = 0.2584746+
0.04449153
=
0.3029661