Teachers' Salaries in North Dakota The average teacher's salary in North Dakota is $35,441. Assume a normal distribution with o=$5100. Round the fina answers to at least 4 decimal places and round Intermediate z-value calculations to 2 decimal places. Part: 0/ 2 Part 1 of 2 What is the probability that a randomly selected teacher's salary is greater than $37,000? P (X > 37,000) =
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![### Teachers' Salaries in North Dakota
**Overview:**
The average teacher's salary in North Dakota is $35,441. We assume a normal distribution with a standard deviation (σ) of $5100. All final answers should be rounded to at least 4 decimal places, and intermediate z-value calculations should be rounded to 2 decimal places.
**Part 1 of 2**
**Question:**
What is the probability that a randomly selected teacher's salary is greater than $37,000?
**Mathematical Expression:**
\[P(X > 37,000) = \]
**Interactive Components:**
- An input box for students to enter their calculated probability.
- Buttons for submission and navigation to the next part of the problem.
**Instructions:**
1. Calculate the z-score using the formula:
\[ z = \frac{X - \mu}{\sigma} \]
where:
- \( \mu \) is the mean salary ($35,441)
- \( \sigma \) is the standard deviation ($5100)
- \( X \) is the salary value in question ($37,000)
2. After finding the z-score, use the z-table to find the corresponding probability.
3. Subtract the z-table value from 1 to find the probability that the salary is greater than $37,000.
**Submission:**
An entry box is provided for the final answer, alongside navigation buttons for progressing to the next part.
**Additional Features:**
A "Next Part" button is included for moving on to subsequent parts of the assignment after completing this section.
**Visual Aids:**
No graphs or diagrams are present in this section, focusing on the calculation process.
This content-setting ensures students comprehend the statistical concepts spanning normal distribution, z-scores, and probability calculations in a structured learning environment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02edcb37-a5b4-4ad7-814d-fe9fafc40457%2Fb829ce9e-7016-4a42-b63d-371e363a54c1%2Fl8zsrbr_processed.jpeg&w=3840&q=75)
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