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A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters.

Find the probability that more than 11 of the eligible voters sampled will vote in the next presidential election.

.772

.228

.608

.113

.887

To solve this problem, we are dealing with a **binomial distribution** because we are considering the probability of "success" (i.e., voting) in a fixed number of trials (20 eligible voters), with a constant probability of success (70%, or \( p = 0.70 \)).

We are asked to find the probability that **more than 11** of the 20 eligible voters sampled will vote.

### Key Parameters:
- \( n = 20 \) (number of trials)
- \( p = 0.70 \) (probability of success)
- \( X \) is the random variable representing the number of voters who will vote, and \( X \sim Binomial(n=20, p=0.70) \).
- We need \( P(X > 11) \), i.e., the probability that more than 11 voters vote.

From the image, the table you provided seems to contain binomial probabilities or cumulative probabilities for different values of \( n \) and \( p \).

### Steps:
1. Look at the portion of the table for \( n = 20 \) and \( p = 0.70 \).
2. Locate the cumulative probability for \( X \leq 11 \), and subtract this from 1 to get \( P(X > 11) \).

Let's interpret the table:

- The \( X = 11 \) row for \( n = 20 \) and \( p = 0.70 \) gives us a cumulative probability (at the \( P \) value of 0.70). 
- Using this approach, \( P(X > 11) = 1 - P(X \leq 11) \).

### Calculation:
From the table provided in your image for \( n = 20 \) and \( p = 0.70 \):
- \( P(X \leq 11) = 0.113 \) (as found from the table for \( X = 11 \)).

Thus, the probability that more than 11 voters will vote is:
\[
P(X > 11) = 1 - P(X \leq 11) = 1 - 0.113 = 0.887
\]

### Final Answer:
The probability that more than 11 of the 20 eligible voters sampled will vote is **0.887**.

Would you like more details on this solution? Here are some relative questions to explore further:

1. How do you calculate probabilities for a binomial distribution manually?
2. What other scenarios could use binomial distribution?
3. How would the solution change if the sample size increased?
4. What is the difference between cumulative probabilities and individual probabilities?
5. How can we approximate binomial probabilities for large sample sizes?

**Tip**: Binomial distribution is often approximated by a normal distribution when the sample size is large.

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Find the probability that more than 11 of the eligible voters sampled will vote in the next presidential election.

Solve a binomial probability question: Find the probability that more than 11 of 20 randomly selected eligible voters will vote in the next presidential election, given that 70% of voters are expected to vote. This solution covers binomial distribution concepts and the use of cumulative probability tables.

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