Question

In 1970, 83% of 30-year-olds in a country earned more than their parents did at age 30(adjusted for inflation). In 2014, only 46% of 30-year-olds in the same country earnedmore than their parents did at age 30. Complete parts a to d below.(a) What is the probability a randomly selected 30-year-old in 1970 earned more thanhis or her parents at age 30?The probability is(Round to four decimal places as needed.)(b) What is the probability that two randomly selected 30-year-olds in 1970 earnedmore than their parents at age 30?The probability is a(Round to four decimal places as needed.)(c) What is the probability that out of ten randomly selected 30-year-olds in 1970, atleast one did not earn more than his or her parents at age 30?The probability is(Round to four decimal places as needed.)(d) What is the probability that out of ten randomly selected 30-year-olds in 2014, atleast one did not earn more than his or her parents at age 30?The probability is(Round to four decimal places as needed.)

Answer 1

Part a) If in 1970 the 83% of 30-year-olds earned more than their parents, then if we choose at random one 30-year-old person the probability that he/she earned more than his/her parents when they were 30 years old is 0.8300.

Part b) The probability of two randomly selected 30-year-olds in 1970 earned more than their parents at age 30 is 0.83*0.83= 0.6889.

Part c) For this part we use binomial probability. The probability of interest is equal to the probability that at least 9 earned more than their parents. The probability that at least 9 earned more than their parents is:

`\begin{gathered} P(x\ge9)=P(x=9)+P(x=10) \\ =(10!)/((10-10)!10!)(0.83)^(10)\cdot(1-0.83)^(10-10)+(10!)/((10-9)!9!)(0.83)^9\cdot(1-0.83)^(10-9) \\ =0.83^(10)+10(0.83)^9(0.17) \end{gathered}`

computing we get 0.4730.

Part d) Solving similarly as part c) but considering that the probability for the year 2014 instead of the one for 1970 we get:

`\begin{gathered} P(x\ge9)=P(x=9)+P(x=10) \\ =(0.46)^(10)+10(0.46)^9(0.54) \end{gathered}`

computing we get 0.0054.