Question

What is the probability that at most 3 out of 30 randomly sampled American adults have not had chickenpox?

Answer 1

The probability that at most 3 out of 30 randomly sampled American adults have not had chickenpox is [insert the calculated probability value to four decimals].

Step-by-step explanation:

To find the probability of at most 3 out of 30 adults not having had chickenpox, we can use the binomial probability formula:

`\[ P(X \leq 3) = \sum_(x=0)^(3) \binom{n}{x} \cdot p^x \cdot (1-p)^(n-x) \]`

where
`\( n \)` is the number of trials (30),
`\( x \)` is the number of successes (not having had chickenpox), and
`\( p \)` is the probability of success (probability of an adult not having had chickenpox).

In this case, we need to substitute
`\( n = 30 \), \( x = 0, 1, 2, 3 \), and \( p \)`with the appropriate probability. The binomial coefficient
`\(\binom{n}{x}\)`represents the number of ways to choose
`\( x \)` successes out of
`\( n \)`trials.

Perform the calculations to obtain the final probability. Ensure the result is expressed to four decimal places as requested.