Project #72143 - normal probability

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


A. Use the z-table to determine the following probabilities. Sketch a normal curve for each problem with the appropriate probability area shaded. 

1. P(z > 2.34)

2. P(z < -1.56)

3. P(z = 1.23)

4. P(-1.82 < z < 0.79)

5. Determine the z-score that corresponds with a 67% probability.     


B.  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 mean µ = 26.1 kg and standard deviation σ = 4.2 kg. Let x be the weight of a fawn in kilograms.  


Complete each of the following steps for the word problems below: ï‚·

Rewrite each of the following word problems into a probability expression, such as P(x>30).  ï‚·

Convert each of the probability expressions involving x into probability expressions involving z, using the information from the scenario. ï‚·

Sketch a normal curve for each z probability expression with the appropriate probability area shaded. ï‚·

Solve the problem.  
1. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs less than 25 kilograms?

2. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs more than 19 kilograms?

3. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs between 30 and 38 kilograms?

4. 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.

5. 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. 

Subject Mathematics
Due By (Pacific Time) 05/26/2015 08:00 pm
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