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