Given that z is a standard normal random variable, compute the following probabilities: a. P (z ≤ - 1) b. P (z >.95) c. P (z ≥ - 1.5) d. P (-.5 ≤ z ≤ 1.75) e. P (1 < z ≤ 3)

Question

Mathematics

Tripp Johnson

9 April, 17:36

Given that z is a standard normal random variable, compute the following probabilities: a. P (z ≤ - 1) b. P (z >.95) c. P (z ≥ - 1.5) d. P (-.5 ≤ z ≤ 1.75) e. P (1 < z ≤ 3)

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Answers (1)

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Emiliano Phillips · Answer 1

Step-by-step explanation:

Given that Z is a standard normal variate.

We are to calculate the probabilities as given

F (z) represents the cumulative probability i. e. P (Z
a. P (z ≤ - 1)

=F (-1)

= 0.158655

b. P (z >.95)

= 1-F (0.95)

= 0.1711

c. P (z ≥ - 1.5)

= 1-F (-1.5)

= 0.9332

d. P (-.5 ≤ z ≤ 1.75)

=F (1.75) - F (-0.5)

= 0.6514

e. P (1 < z ≤ 3)

=F (3) - F (1)

=0.1573