one source told me it is 0.159,another said it is 0.3503, cross check and carefully double check and tell me which is right

Let's carefully re-calculate the probabilities for selecting exactly 8 and exactly 9 students, and then sum them to ensure accuracy.

### Given:
- Number of students \( n = 36 \)
- Probability of selection \( p = 0.28 \)
- \( k = 8 \) and \( k = 9 \) are the numbers of selected students we're interested in.

### Binomial Probability Formula Recap:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]

### Step-by-Step Calculation:
1. Compute \( P(X = 8) \) using the binomial formula.
2. Compute \( P(X = 9) \).
3. Sum these two probabilities to find the total probability \( P(8 \text{ or } 9) \).

I'll recalculate these values for you.After carefully recalculating:

- The probability \( P(X = 8) \) is approximately **0.116**.
- The probability \( P(X = 9) \) is approximately **0.140**.
- The total probability \( P(8 \text{ or } 9) \) is **0.256** (or 25.6%).

This confirms that the correct probability is approximately **0.256**. The other values you encountered (0.159 and 0.3503) are incorrect.

Would you like further explanation or have any other questions?

Here are 8 more related questions:

1. How would the calculations change if the sample size were different, say 50 students?
2. What would happen if the probability of each student being selected changed to 0.5?
3. Can we approximate the binomial distribution with a normal distribution in this case?
4. How does the binomial distribution apply to real-world scenarios beyond this problem?
5. What are some common errors to avoid when calculating binomial probabilities?
6. How can technology, like graphing calculators or software, simplify these calculations?
7. How do changes in the number of trials impact the shape of the binomial distribution?
8. What is the probability that fewer than 5 students will be selected?

**Tip:** When working with binomial probabilities, it's crucial to ensure that all parameters (like \( n \), \( k \), and \( p \)) are used consistently throughout the calculation.

Explore how to calculate binomial probabilities for selecting students with a step-by-step solution. Understand the binomial probability formula and its application in real-world scenarios. Probability of selecting exactly 8 and 9 students given sample size of 36 and probability of selection 0.28. Correct probability approximately 0.256.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation