39.6% of consumers believe that cash will be obsolete in the next 20 years. Assume that 8 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.
The probability is
(Round to three decimal places as needed.)

This problem involves a **binomial distribution** because there are a fixed number of trials (8 consumers), two possible outcomes (believe cash will be obsolete or not), and a fixed probability of success (39.6%).

The formula for the binomial probability is:

\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]

Where:
- \( n = 8 \) (number of trials)
- \( p = 0.396 \) (probability of success)
- \( k \) is the number of successes

To find the probability that fewer than 3 consumers believe that cash will be obsolete, we need to calculate:

\[
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
\]

I'll calculate each of these probabilities and sum them up.The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is **0.324**.

Would you like more details or have any questions?

Here are 5 related questions that might interest you:
1. What is the probability that exactly 3 consumers believe cash will be obsolete?
2. How would the probability change if the sample size were increased to 10 consumers?
3. What is the expected number of consumers who believe cash will be obsolete out of 8?
4. What is the probability that at least 5 consumers believe cash will be obsolete?
5. How does the probability distribution look for all possible outcomes from 0 to 8?

**Tip:** When dealing with binomial distributions, remember that probabilities can be found for ranges of outcomes by summing individual probabilities within the range.

39.6% of consumers believe that cash will be obsolete in the next 20 years. Assume that 8 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. The probability is (Round to three decimal places as needed.)

Solve the probability problem where 39.6% of consumers believe cash will be obsolete in 20 years. Given a sample of 8 consumers, find the probability that fewer than 3 believe this statement. This problem involves binomial distribution concepts, suitable for Grades 10-12.

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