Question

After Rob Ford, the mayor of Toronto, announced his plans to cut budget costs in late $2011$, the Forum Research polled $1,046$people to measure the mayor’s popularity. Everyone polled expressed either approval or disapproval. These are the results their poll produced:

• In early $2011,60$percent of the population approved of Mayor Ford’s actions in office.

• In mid-$2011,57$percent of the population approved of his actions.

• In late $2011$, the percentage of popular approval was measured at $42$percent.

a. What is the sample size for this study?

b. What proportion in the poll disapproved of Mayor Ford, according to the results from late $2011$?

c. How many people polled responded that they approved of Mayor Ford in late $2011$?

d. What is the probability that a person supported Mayor Ford, based on the data collected in mid-$2011$?

e. What is the probability that a person supported Mayor Ford, based on the data collected in early $2011$?

Short answer

(a) The sample study for the given statement is $n\left(S\right)=1046$.

(b) The proportion in the poll disapproved mayor ford from late $2011$is, $58\%$.

(c) The people who approved mayor ford from late $2011\text{is},439\text{people}$.

(d) The probability of people who approved mayor ford from mid $2011\text{is},0.57$.

(e) The probability of people who approved mayor ford from early$2011\text{is},0.6$.

Step-by-step solution

Given information (a)

There are $1046$people.

In $2011$, $60\%$approved.

In mid-$2011$, $57\%$approved.

In late $2011$, $42\%$approved.

Explanation (part a)

The sample space for the given statement is,

Let the number of people polled to measure be S.

$n\left(s\right)=1046$

Given information (part b)

There are $1046$people.

In $2011$, $60\%$approved.

In mid-$2011$, $57\%$approved.

In late $2011$, $42\%$approved.

Explanation (part b)

In late $2011$, $42\%$of people approved.

The proportion of disapproval of mayor ford in late $2011$is,

localid="1648919657772" $$\begin{gathered} 1-0.42=0.58 \\ =58\% \end{gathered}$$

Given information (part c)

There are $1046$people.

In $2011$, $60\%$approved.

In mid-$2011$, $57\%$approved.

In late $2011$, $42\%$approved.

Explanation (part c)

In late $2011$, $42\%$of people approved.

The people who approved mayor ford from late $2011$is,

$\frac{42}{100}\times 1046=439\text{people}$

Given information (part d)

There are $1046$people.

In $2011$, $60\%$approved.

In mid-$2011$, $57\%$approved.

In late $2011$, $42\%$approved.

Explanation (part d)

In mid-$2011$, $57\%$of people approved.

The probability of people who approved mayor ford from mid$2011$

$\frac{57}{100}=0.57$

Given information (part e)

There are $1046$people.

In $2011$, $60\%$approved.

In mid-$2011$, $57\%$approved.

In late $2011$, $42\%$approved.

Explanation (part e)

In mid-$2011$, $60\%$of people approved.

The probability of people who approved mayor ford from early$2011$

$\frac{60}{100}=0.6$