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Assume z is a standard normal random variable. Compute the following probabilities.

- a. P(–1.33 ≤ z ≤ 1.67)
- b. P(1.23 ≤ z ≤ 1.55)
- c. P(z ≥ 2.32)
- d. P(z ≥ –2.08)
- e. P(z ≥ –1.08)

The principle that applies to the normal distribution of probability allows to determine the probability for the random variables that are normal. For instance 95% of normally distributed data is within the two standard deviations from the average.

a)P ( – 1.33 < Z < 1.67 ) = P ( Z < 1.67 ) – P ( Z < – 1.33 )

By Using Standard Normal Table,

P ( – 1.33 < Z < 1.67 ) = 0.9525 – 0.0918

P ( – 1.33 < Z < 1.67 ) = 0.8607b)P ( 1.23 < Z < 1.55 ) = P ( Z < 1.55 ) – P ( Z < 1.23 )

By Using Standard Normal Table,

P ( 1.23 < Z < 1.55 ) = 0.9394 – 0.8907

P ( 1.23 < Z < 1.55 ) = 0.0487c)P ( Z > 2.32 ) = 1 – P ( Z < 2.32 )

By Using Standard Normal Table,

P ( Z > 2.32 ) = 1 – 0.9898

P ( Z > 2.32 ) = 0.0102d)By Using Standard Normal Table,

P ( Z < – 2.08 ) = 0.0188e)By Using Standard Normal Table,

P ( Z < – 1.08 ) = 0.1401