At a large university, 55% of the students frequently visit the university's bookstore.  If 15 students are randomly selected, what is the probability that exactly 11 frequently visit the bookstore?   

Round your answer to 3 decimal places. 

This problem is a classic binomial probability problem where we are given:

- The probability of success (\( p \)) is 55% or 0.55 (students visiting the bookstore).
- The number of trials (\( n \)) is 15 (students selected).
- The number of successes (\( k \)) is 11 (students who visit the bookstore).

The binomial probability formula is given by:

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

Where:
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n - k)!} \).
- \( p^k \) is the probability of exactly \( k \) successes.
- \( (1 - p)^{n - k} \) is the probability of exactly \( n - k \) failures.

Now, we can substitute the values:

- \( n = 15 \)
- \( k = 11 \)
- \( p = 0.55 \)
- \( 1 - p = 0.45 \)

Let's calculate the probability.The probability that exactly 11 out of 15 students frequently visit the bookstore is \( 0.078 \), or 7.8%.

Would you like further details or have any questions about this process?

Here are some related questions for further practice:
1. What is the probability that exactly 10 students frequently visit the bookstore?
2. What is the probability that at least 11 students frequently visit the bookstore?
3. What is the expected number of students who frequently visit the bookstore?
4. What is the probability that fewer than 8 students visit the bookstore?
5. How would the probability change if the probability of visiting the bookstore was 60% instead of 55%?

**Tip:** Binomial probabilities can be quickly computed when using proper tools like factorial functions or probability tables.

At a large university, 55% of the students frequently visit the university's bookstore. If 15 students are randomly selected, what is the probability that exactly 11 frequently visit the bookstore? Round your answer to 3 decimal places.

Learn how to calculate the binomial probability that exactly 11 out of 15 students frequently visit a university bookstore, given that 55% of the students visit the store. This step-by-step solution covers the binomial distribution formula and key concepts in probability, suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation