About 9% of the population has a particular genetic mutation. 100 people are randomly selected.

Find the mean for the number of people with the genetic mutation in such groups of 100.

To find the mean number of people with the genetic mutation in a group of 100, you can use the formula for the mean of a binomial distribution:

\[
\mu = n \cdot p
\]

where:
- \( n \) is the total number of people (in this case, \( n = 100 \)),
- \( p \) is the probability that a randomly selected person has the genetic mutation (in this case, \( p = 0.09 \)).

Now, applying the values:

\[
\mu = 100 \cdot 0.09 = 9
\]

So, the mean number of people with the genetic mutation in such groups of 100 is 9.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the standard deviation for the number of people with the mutation in this group?
2. How would the mean change if the probability of having the mutation increased to 15%?
3. What is the probability of exactly 9 people having the mutation in this group of 100?
4. How does the binomial distribution relate to the normal distribution for large sample sizes?
5. What are some other examples of real-world problems modeled by the binomial distribution?

**Tip:** The binomial distribution is often used to model situations where there are two possible outcomes, like success/failure, yes/no, or mutation/no mutation.

About 9% of the population has a particular genetic mutation. 100 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 100.

Learn how to calculate the mean number of people with a genetic mutation in a group of 100 using binomial distribution. This problem involves probability and the binomial theorem, suitable for high school students. Find the mean with a simple formula: μ = n * p, where p = 0.09 and n = 100.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation