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)

1. P(z < -1.56)

1. P(z = 1.23)

1. P(-1.82 < z < 0.79)

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

Read the following scenario:

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?

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

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

1. 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.

1. 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.