Question

the responses of 1322 voters to a survey about the way the media conducted themselves in a recent political campaign are shown in the accompanying pareto chart. find the probability of each event listed in parts (a) through (d) below.

(a) randomly selecting a person from the sample who did not give the media an a or a b

the probability is \square.
(type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Identify total sample size

Using the Pareto Chart knowledge point
The total number of surveyed voters is given in the problem statement:

$$ N = 1322 $$

Identify favorable outcomes

Using the Complementary Events and Pareto Chart knowledge points
We want to find the number of respondents who did not give the media an A or B.
From the Pareto chart, the number of respondents who gave an "A or B" is:

$$ n(\text{A or B}) = 301 $$

Therefore, the number of respondents who did not give an A or B is:

$$ n(\text{not A or B}) = N - n(\text{A or B}) = 1322 - 301 = 1021 $$

Calculate empirical probability

Using the Empirical Probability knowledge point

$$ P(\text{not A or B}) = \frac{n(\text{not A or B})}{N} = \frac{1021}{1322} \approx 0.7723147 $$

Round to three decimal places

Using the Empirical Probability knowledge point
Rounding \(0.7723147\) to three decimal places gives:

$$ P \approx 0.772 $$

Answer:

(a) Randomly selecting a person from the sample who did not give the media an A or B

The probability is <blank>0.772</blank>.
(Type an integer or a decimal. Round to three decimal places as needed.)