Question

Given graph :

The graph in the figure displays the sample sizes and percentages of people in different age and gender groups who were polled concerning their approval of Mayor Ford’s actions in office. The total number in the sample of all the age groups is$1045.$

a. Define three events in the graph.

b. Describe in words what the entry $40$means.

c. Describe in words the complement of the entry in question $2.$

d. Describe in words what the entry 30 means.

e. Out of the males and females, what percent are males?

f. Out of the females, what percent disapprove of Mayor Ford?

g. Out of all the age groups, what percent approve of Mayor Ford? h. Find P(Approve|Male).

i. Out of the age groups, what percent are more than $44$years old?

j. Find $P\left(Approve\right|Age<35).$

Short answer

a. Three events in the graph are:

1. The individual is male.
2. The individual approves of Mayor Ford.
3. The individuals is from age group $34-44.$

b. The entry $40$means that total $0.40$percentage of individual approves Mayor Ford.

c. Complement of entry $40$means that total $0.60$percentage of individual disapproves Mayor Ford.

d. The entry $30$means that total $0.30$percentages of age groups $18-34$approves Mayor Ford.

e. From the graph we can say that, there are $0.44$percentages of males, out of the males and females.

f. From the graph, we can observe that out of the females, there are $0.63$percentages disapprove of Mayor Ford.

g. From the graph, we can observe that out of the age groups, there are percentages approve of Mayor Ford.

h. From the graph, we can observe that the total percentage of males who approve Mayor Ford is $0.44.$

i. The total percentage which are more than $44$years old

$$\begin{gathered} =\frac{226+268+331}{1045} \\ =\frac{825}{1045} \\ =0.7895 \end{gathered}$$

Hence, the total percentage which is more than $44$years old is $0.7835.$

j. From the graph, we can observe that there is total $0.30$percentage of those individuals are present in the age less than$35$ and approve Mayor Ford.

Hence, $\mathrm{P}(Approve\mid age<35)=0.30$.

Step-by-step solution

Given information

Given table

The following graph displays the sample sizes and percentages of people in different age and gender groups who were polled concerning their approval of Mayor Ford's actions in office. The total number in the sample of all the age groups is 1045.a. Three events in the graph are:The individual is male.The individual approves of Mayor Ford.The individuals is from age group 34-44.b. The entry 40 means that total 0.40percentage of individual approves Mayor Ford.c. The entry 30 means that total 0.30 percentages of age groups 18-34 approves Mayor Ford.d. From the graph we can say that, there are 0.44 percentages of males, out of the males and females.e. From the graph, we can observe that out of the females, there are $0.63$ percentages disapprove of Mayor Ford.f. From the graph, we can observe that out of the age groups, there are $0.40$ percentages approve of Mayor Ford.g. From the graph, we can observe that the total percentage of males who approve Mayor Ford is $0.44$.The total percentage which are more than 44 years oldHence, the total percentage which is more than 44 years old is $0.7895$.From the graph, we can observe that there is total $0.30$ percentage of those individuals are present in the age less than 35 and approve Mayor Ford.Hence, $\mathrm{P}($ Approve $\mid$ age $<35)=0.30$.

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