Statistics

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 s = 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 in to a probability expression, such as P(x>30).

·       ·  Convert each of the probability expressions involving x into probabilityexpressions 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.

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

·Whatistheprobabilityofselectingafawnlessthan6monthsoldin Yellowstone that weighs more than 19 kilograms?

·Whatistheprobabilityofselectingafawnlessthan6monthsoldin Yellowstone that weighs between 30 and 38 kilograms?

·If a fawn less than 6months old weighs16 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 6months old that corresponds with a 20% probability of being randomly selected?

· Explain and verify your answer mathematically.

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