3) Suppose in MSU, 12 out of 200 students are covid positive. If 300 students are selected for COVID test, find 1

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### Problem Statement

Suppose in MSU, 12 out of 200 students are COVID positive. If 300 students are selected for COVID testing, find the probability that less than 18 students were COVID positive.

### Explanation

To solve this problem, you can use the principles of probability and statistics. The solution will involve comparing the known ratio of COVID-positive students to the larger sample size of 300 to determine the likelihood of having fewer than 18 students test positive.

**Steps to Consider:**

1. **Calculate the Probability of a Student Being COVID Positive:**
   - Use the initial data to determine the probability of any single student being COVID positive.
   - Probability \( p = \frac{12}{200} \).

2. **Use Probability Distribution:**
   - For larger samples, you can use binomial or normal approximation to estimate this probability.
   - Calculate the expected number and standard deviation.

3. **Find the Probability for 300 Students:**
   - Calculate the probability for fewer than 18 students being positive in the group of 300.
   - Use appropriate statistical tools or methods such as a binomial calculator or normal distribution table.

Through these mathematical concepts, the solution will reveal the probability value, helping us understand the likelihood of this scenario in a broader context at MSU.
Transcribed Image Text:### Problem Statement Suppose in MSU, 12 out of 200 students are COVID positive. If 300 students are selected for COVID testing, find the probability that less than 18 students were COVID positive. ### Explanation To solve this problem, you can use the principles of probability and statistics. The solution will involve comparing the known ratio of COVID-positive students to the larger sample size of 300 to determine the likelihood of having fewer than 18 students test positive. **Steps to Consider:** 1. **Calculate the Probability of a Student Being COVID Positive:** - Use the initial data to determine the probability of any single student being COVID positive. - Probability \( p = \frac{12}{200} \). 2. **Use Probability Distribution:** - For larger samples, you can use binomial or normal approximation to estimate this probability. - Calculate the expected number and standard deviation. 3. **Find the Probability for 300 Students:** - Calculate the probability for fewer than 18 students being positive in the group of 300. - Use appropriate statistical tools or methods such as a binomial calculator or normal distribution table. Through these mathematical concepts, the solution will reveal the probability value, helping us understand the likelihood of this scenario in a broader context at MSU.
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