3. Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. a. If ONE teacher is randomly drawn from this population what is the probability their salary is less than $40,000? b. If 10 teachers are randomly selected from this population, find the probability that their mean salary is between $45K and $46K. c. If we didn't know the nature of the original distribution would we be able to calculate the probability in part b? Support your answer.

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**Problem 3: Statistical Analysis of Teacher Salaries**

This problem explores the statistical distribution of teacher salaries in an elementary school district. The salaries are normally distributed with a given mean and standard deviation.

- **Mean Salary (μ)**: $44,000
- **Standard Deviation (σ)**: $6,500

**Questions:**

**a. Individual Salary Probability**

Determine the probability that a randomly selected teacher's salary is less than $40,000.

**b. Group Mean Salary Probability**

When selecting 10 teachers randomly, calculate the probability that their average salary falls between $45,000 and $46,000.

**c. Distribution Knowledge**

Discuss whether it's possible to calculate the probability in part b if the original distribution was unknown. Provide justification for your answer.
Transcribed Image Text:**Problem 3: Statistical Analysis of Teacher Salaries** This problem explores the statistical distribution of teacher salaries in an elementary school district. The salaries are normally distributed with a given mean and standard deviation. - **Mean Salary (μ)**: $44,000 - **Standard Deviation (σ)**: $6,500 **Questions:** **a. Individual Salary Probability** Determine the probability that a randomly selected teacher's salary is less than $40,000. **b. Group Mean Salary Probability** When selecting 10 teachers randomly, calculate the probability that their average salary falls between $45,000 and $46,000. **c. Distribution Knowledge** Discuss whether it's possible to calculate the probability in part b if the original distribution was unknown. Provide justification for your answer.
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