Question

A poll showed that 57.4% 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 your answer as a decimal accurate to 3 decimal places.

Answer 1

Probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life = 0.426 .

Explanation:

We are given that a poll showed that 57.4% of Americans say they believe that statistics teachers know the true meaning of life.

Let the above probability that % of Americans who believe that statistics teachers know the true meaning of life = P(A) = 0.574

Now, probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is given by = 1 - Probability of randomly selecting someone who believe that statistics teachers know the true meaning of life = 1 - P(A)

So, required probability = 1 - 0.574 = 0.426 .

Answer 2

The probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 0.426.

Explanation:

Let X = number of Americans who believe that statistics teachers know the true meaning of life.

The probability of the random variable X is,

P (X) = 0.574

The event of a person not believing that statistics teachers know the true meaning of life is the complement of the event X.

The probability of the complement of an event, E is the probability of that event not happening.

`P(E^(c))=1-P(E)`

Compute the value of
`P(X^(c))` as follows:

`P(X^(c))=1-P(X)\\=1-0.574\\=0.426`

Thus, the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 0.426.