A. What is the probability that Z > 1? B.What is the probability that Z > 1.5? C

Question

A. What is the probability that Z > 1?

B.What is the probability that Z > 1.5?

C. What is the probability that a random variable with a normal distribution will be within 1.5 standard deviations of its mean?

D.What is the probability that a random variable with a normal distribution will be within 0.5 standard deviations of its mean?

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Explanation / Answer

A. What is the probability that Z > 1?

Answer: Pr(Z > 1) = 1 - Pr(Z <1) = 1 - 0.8413 = 0.1587

B.What is the probability that Z > 1.5?

Answer : Pr(Z > 1.5) = 1 - Pr(Z < 1.5) = 1 - 0.9332 = 0.0668

C. What is the probability that a random variable with a normal distribution will be within 1.5 standard deviations of its mean?

Answer: Pr( -1.5 < Z < 1.5) = Pr(Z < 1.5) - Pr(Z < -1.5) = 0.9332 - 0.0668 = 0.8664

D.What is the probability that a random variable with a normal distribution will be within 0.5 standard deviations of its mean?

Answer : Pr( -0.5 < Z < 0.5) = Pr(Z < 0.5) - Pr(Z < -0.5) = 0.6915- 0.3085 = 0.3830

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