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In the image, you are working on a probability question using the binomial distribution.

Let's break down the relevant parts:

1. **Given Information**:
   - 36% of 18- to 29-year-olds in the population own a tablet.
   - You are surveying 6 people (sample size = 6).

2. **Part c**: The probability that at least four out of the six surveyed will own a tablet is given as **0.1286**.

3. **Part d**:
   - To find the mean and standard deviation of the number of 18- to 29-year-olds who own a tablet out of six surveyed.

**Mean of a Binomial Distribution**:
The formula for the mean \(\mu\) of a binomial distribution is:
\[
\mu = n \times p
\]
where:
- \(n = 6\) (the number of trials, i.e., the sample size),
- \(p = 0.36\) (the probability of owning a tablet).

Let's calculate the mean:
\[
\mu = 6 \times 0.36 = 2.16
\]
Thus, the mean number of 18- to 29-year-olds who own a tablet in a survey of six is **2.16**.

**Standard Deviation of a Binomial Distribution**:
The formula for the standard deviation \(\sigma\) is:
\[
\sigma = \sqrt{n \times p \times (1 - p)}
\]
Substituting the given values:
\[
\sigma = \sqrt{6 \times 0.36 \times (1 - 0.36)} = \sqrt{6 \times 0.36 \times 0.64}
\]

I will now calculate the standard deviation.The standard deviation of the number of 18- to 29-year-olds who own a tablet out of six surveyed is approximately **1.1758** (rounded to four decimal places).

To summarize:
- The mean number of people who own a tablet in a survey of six is **2.16**.
- The standard deviation is **1.1758**.

Do you need more details or have any questions? Here are some related questions:

1. How is the binomial distribution applied in real-world surveys?
2. How would the results change if the sample size increased?
3. What is the probability that exactly four people own a tablet?
4. How does the probability change if the percentage of tablet owners increases to 50%?
5. Can we apply a normal approximation to this binomial distribution?

**Tip**: Always check the conditions for using the binomial distribution (e.g., fixed number of trials, independent events, and consistent probability).

A recent survey reported that 36% of 18- to 29-year-olds in a certain country own tablets. Using the binomial distribution, complete parts (a) through (e) below. What is the probability that in the next six 18- to 29-year-olds surveyed, at least four will own a tablet? What are the mean and standard deviation of the number of 18- to 29-year-olds who will own a tablet in a survey of six?

This problem involves a binomial distribution where 36% of young adults aged 18-29 own tablets. It asks for the probability that at least four out of six surveyed own a tablet, and it calculates the mean and standard deviation of the number of tablet owners in a sample size of six. Learn how to solve using the binomial probability formula.

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