**INSTRUCTIONS: **

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**This is not to be written as a paper. Please insert the answers to the questions on this document.****Showing work is required!****If tables are required insert them.****If Excel is used please attach the work book and label each tab with the problem and question it represents. Ensure all data is there including formulas.****If a sketch is required please ensure it is scanned and labeled accordingly. Thank you!****J**

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**WK3 WS1Discrete Probability Distributions **

**Read the following scenario and complete each of the four problem sets below:**

Suppose the distribution below represents the probability of a person to make a certain grade in Chemistry 101, where x = the letter grade of the student in the class (A=4, B=3, C=2, 0=1, F=O).

- Is this an example of a valid probability distribution? Explain your answer.
- Determine the probability that a student selected at random would make a C or higher in Chemistry 101.
- Determine the mean and standard deviation of the grade distribution.
- Make a NEW table that shows only the probability of students passing or failing (i.e. receiving an F) Chemistry 101.
- “A professor has 30 students in his or her Chemistry 101 course and wants to determine the probability that a certain number of these 30 students will pass his or her course.”Does this represent a binomial experiment? Explain your answer.
- Based on the Pass/Fail table, what is the probability that 24 of the 30 students enrolled in Chemistry 101 during the spring semester will pass the course?
- Determine the mean and standard deviation of the data in the Pass/Fail table.

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**WK3 WS2Nominal Probability **

**Read the following scenario and complete each of the four problem sets below:**

- Use the z-table to determine the following probabilities.
a normal curve for each problem with the appropriate probability area shaded.__Sketch__ - P(z > 2.34)
- P(z < -1.56)
- P(z = 1.23)
- P(-1.82 < z < 0.79)
- Determine the z-score that corresponds with a 67% probability.

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- Read the following scenario:

Park Rangers in a Yellowstone National Park have determined that fawns less than 6 months old have a body weight that is approximately normally distributed with a meanµ = 26.1 kg and standard deviation a = 4.2 kg. Let x be the weight of a fawn in kilograms.

Complete each of the following steps for the word problems below:

- Rewrite each of the following word problems into a probability expression, such as P(x>30).
- Convert each of the probability expressions involving x into probability expressions involving z, using the information from the scenario.
a normal curve for each z probability expression with the appropriate probability area shaded.__Sketch__- Solve the problem.

- What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs less than 25 kilograms?
- What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs more than 19 kilograms?
- What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs between 30 and 38 kilograms?
- If a fawn less than 6 months old weighs 16 pounds, would you say that it is an unusually small animal? Explain and verify your answer mathematically.
- What is the weight of a fawn less than 6 months old that corresponds with a 20% probability of being randomly selected? Explain and verify your answer mathematically.

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