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

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

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

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

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

Expert verified

(a) The sample study for the given statement is nS=1046.

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

(c) The people who approved mayor ford from late 2011is,439people.

(d) The probability of people who approved mayor ford from mid 2011is,0.57.

(e) The probability of people who approved mayor ford from early2011is,0.6.

Step by step solution

01

Given information (a)

There are 1046people.

In 2011, 60%approved.

In mid-2011, 57%approved.

In late 2011, 42%approved.

02

Explanation (part a)

The sample space for the given statement is,

Let the number of people polled to measure be S.

ns=1046

03

Given information (part b)

There are 1046people.

In 2011, 60%approved.

In mid-2011, 57%approved.

In late 2011, 42%approved.

04

Explanation (part b)

In late 2011, 42%of people approved.

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

localid="1648919657772" 1-0.42=0.58=58%

05

Given information (part c)

There are 1046people.

In 2011, 60%approved.

In mid-2011, 57%approved.

In late 2011, 42%approved.

06

Explanation (part c)

In late 2011, 42%of people approved.

The people who approved mayor ford from late 2011is,

42100×1046=439people

07

Given information (part d)

There are 1046people.

In 2011, 60%approved.

In mid-2011, 57%approved.

In late 2011, 42%approved.

08

Explanation (part d)

In mid-2011, 57%of people approved.

The probability of people who approved mayor ford from mid2011

57100=0.57

09

Given information (part e)

There are 1046people.

In 2011, 60%approved.

In mid-2011, 57%approved.

In late 2011, 42%approved.

10

Explanation (part e)

In mid-2011, 60%of people approved.

The probability of people who approved mayor ford from early2011

60100=0.6

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