Question

chapter 4.2 homework
score: 40/83 answered: 23/38
question 24
4.2 theoretical probability. complement.
a poll showed that 47.5% of americans say they believe that statistics teachers know the true meaning of life. what is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life.
report the answer as a percent rounded to one decimal place accuracy. you need not enter the “%” symbol.
prob =
question help: video message instructor

Explanation:

Step1: Recall probability - complement rule

The probability of an event $A$ and its complement $\overline{A}$ satisfy $P(A)+P(\overline{A}) = 1$. Here, let $A$ be the event that a person believes that statistics teachers know the true meaning of life, and $P(A)=47.5\%=0.475$.

Step2: Calculate the probability of the complement

We want to find $P(\overline{A})$. Using the formula $P(\overline{A})=1 - P(A)$. Substitute $P(A) = 0.475$ into the formula, so $P(\overline{A})=1 - 0.475=0.525$.

Step3: Convert to percentage and round

To convert the decimal to a percentage, multiply by 100: $0.525\times100 = 52.5\%$. Rounding to one - decimal place, the result is still $52.5$.

Answer:

52.5