Question

a group of marketing researchers for a popular cell phone manufacturer collected the following information about young adults (aged 18 - 25): 1% use a cell phone that is 3 years or older, 2% use a cell phone that is 2 - 3 years old, 20% use a cell phone that is 1 - 2 years old, and 77% use a cell phone that is less than 1 year old. suppose a young adult was selected at random. let x equal the age of a randomly selected persons cell phone. which of the following is the probability distribution for the age of that persons cell phone? <1 1 ≤ x < 2 2 ≤ x < 3 ≥ 3 0.77 0.20 0.2 0.1 <1 1 ≤ x < 2 2 ≤ x < 3 ≥ 3 0.01 0.02 0.20 0.77 <1 1 ≤ x < 2 2 ≤ x < 3 ≥ 3 0.25 0.25 0.25 0.25 <1 1 ≤ x < 2 2 ≤ x < 3 ≥ 3 0.77 0.20 0.02 0.01

Explanation:

Step1: Match the probabilities with the intervals

The problem states that \(77\%\) use a cell phone that is less than \(1\) year old. So \(P(X < 1)=0.77\).

Step2: Match the next probability

It is given that \(20\%\) use a cell phone that is \(1 - 2\) years old. So \(P(1\leq X<2) = 0.20\).

Step3: Match the third probability

It is given that \(2\%\) use a cell phone that is \(2 - 3\) years old. So \(P(2\leq X<3)=0.02\).

Step4: Match the last probability

It is given that \(1\%\) use a cell phone that is \(3\) years or older. So \(P(X\geq3)=0.01\).

Answer:

The probability distribution is \(P(X < 1)=0.77\), \(P(1\leq X<2) = 0.20\), \(P(2\leq X<3)=0.02\), \(P(X\geq3)=0.01\) which corresponds to the last option (the one with \(0.77\), \(0.20\), \(0.02\), \(0.01\) in the respective columns).