Question

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 83 people in the 18-21 age bracket and finds that 70 of them respond and 13 refuse to respond. When 299 people in the 22-29 age bracket are contacted, 284 respond and 15 refuse to respond. Assume that 1 of the 382 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who refused to respond.Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.prob = %

Answer 1

Answer:

The probability of getting someone in the 22-29 age bracket or someone who refused to respond is 81.7%

Step-by-step explanation:

Given:

A pollster contacted people under the age brackets 18-21 and 22-29 to do a survey and recorded the does who responded and didn't.

To find:

the probability of getting someone in the 22-29 age bracket or someone who refused to respond

To answer the question, we will make a table to make it easy:

First, we need to find someone in the age bracket 22-29 or some who refused to respond

Let x = People who are in the 22 - 29 age bracket

Let y = people that do not respond

someone in the age bracket 22-29 or someone who refused to respond = n(x or y)

The formula is given as:

n(x or y) = n(x) + n(y) - n(x and y)

`\begin{gathered} n(x)\text{ = total people in 22-29 age bracket = 299} \\ n(y)\text{ = total people who did not respond = 28} \\ n(x\text{ and y\rparen = people in 22-29 age bracket and didn't respond = 15} \\ \\ n(x\text{ or y\rparen = 299 + 28 - 15} \\ \\ n(x\text{ or y\rparen = 312} \end{gathered}`

Next, we will find the probability of someone in the age bracket 22-29 or some who refused to respond:

Pr(x or y) = n(x or y)/total people surveyed

`\begin{gathered} Total\text{ people surveyed = 382} \\ \\ Pr(x\text{ or y\rparen = }(312)/(382) \\ \\ Pr(x\text{ or y\rparen = 0.8168 = 81.68 \%} \\ \\ Pr(x\text{ or y\rparen = 81.7\% \lparen1 decimal place\rparen} \end{gathered}`