Question

1. Each person in a large group of children with cell phones was asked, "How old were you when you first received acell phone?The responses are summarized in the table below.Age In YearsProbability0.030.0610111213141516170.110.230.230.1400110.080.01a.bMake a graph of the probability distributionThe bar centered at 12 in your graph represents the probability that a randomly selected person in this groupfirst received a cell phone at age 12. What is the area of the bar representing age 127 How does this compareto the probability corresponding to 12 in the table?What do you think the sum of the areas of all of the bars will be? Explain your reasoningWhat is the probability that a randomly selected person from this group first received a cell phone at age 12 or13?Is the probability that a randomly selected person from this group first received a cell phone at an age olderthan 15 greater than or less than the probability that a randomly selected person from this group first receiveda cell phone at an age younger than 12?d.e

Answer 1

Answers:

a. Graph

b. Area = 0.23

c. Sum = 1

d. P = 0.46

e. The probability that a person first received a cellphone at an age older than 15 is less than the probability that a person first received a cellphone at an age younger than 12.

Step-by-step explanation:

a. To make the graph of a probability distribution, we will make a bar graph where the x-axis is the age and the y-axis is the probability. So, the graph is:

b. If each bar has a width of 1 unit and a height equal to the probability, the area of the bar centered at 12 will be equal to:

Area = Width x Height

Area = 1 x 0.23

Area = 0.23

So, the area of the bar is equal to the probability that a child first receives a cellphone at age 12.

c. Since the area of each bar is equal to the respective probability, we get that the sum of the area of all bars should be equal to 1. In fact:

0.03 + 0.05 + 0.11 + 0.23 + 0.23 + 0.14 + 0.11 + 0.08 + 0.01 = 1

d. To know this probability, we need to add the probability that a person first received a cellphone at age 12 and the probability that a person first received a cellphone at age 13. So, the answer for this part will be:

P = P( Age 12) + P(Age 13)

P = 0.23 + 0.23

P = 0.46

e. The probability that a person first received a cellphone at an age older than 15 is equal to:

P(older than 15) = P(Age 16) + P(Age 17)

P(older than 15) = 0.08 + 0.01

P(older than 15) = 0.09

In the same way, the probability that a person first received a cellphone at an age younger than 12 is:

P(younger than 12) = P(Age 9) + P(Age 10) + P(Age 11)

P(younger than 12) = 0.03 + 0.06 + 0.11

P(younger than 12) = 0.2

Since 0.09 is lower than 0.2, we get that the probability that a person first received a cellphone at an age older than 15 is less than the probability that a person first received a cellphone at an age younger than 12.

Therefore, the answers are:

a. Graph

b. Area = 0.23

c. Sum = 1

d. P = 0.46

e. The probability that a person first received a cellphone at an age older than 15 is less than the probability that a person first received a cellphone at an age younger than 12.