Question

Let z denote a random variable that has a standard normal distribution. Determine each of the probabilities below. (Round all answers to four decimal places.)

(b) P(z 2.37) =

(c) P(z < -1.23) =

(d) P(1.14 < z < 3.35) =

(e) P(-0.77 z -0.56) =

(f) P(z > 2) =

(g) P(z -3.28) =

(h) P(z = 1.98)=

Answer 1

Explanation:

We can use a standard normal distribution table or calculator to determine the probabilities. Here are the answers:

(b) P(z > 2.37) = 0.0083

(c) P(z < -1.23) = 0.1093

(d) P(1.14 < z < 3.35) = 0.0473

(e) P(-0.77 < z < -0.56) = 0.0749

(f) P(z > 2) = 0.0228

(g) P(z < -3.28) = 0.0005

(h) P(z = 1.98) = 0 (since the normal distribution is continuous, the probability of a single point is zero).