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the z-table to determine the following probabilities. Sketch a normal curve for each problem with the appropriate probability area shaded. P(z > 2.34) P(z <

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

Park Rangers in Yellowstone National Park have determined that fawns less than 6 months old have a body weight that is approximately normally distributed with a mean = 26.1 kg and standard deviation = 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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