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.)

P(z ≤ 2.37)
P(1.14 < z < 3.35)
P(-0.77≤ z ≤-0.56)
P(z≥ -3.28)

Answer 1

P(z ≤ 2.37) = 0.9910,

P(1.14 < z < 3.35) = 0.1284,

P(-0.77≤ z ≤-0.56) = 0.0644,

P(z≥ -3.28) = 0.9995.

Explanation:

Answer 2

Explanation:

Using a standard normal table or calculator, we can determine the probabilities as follows:

(a) P(z ≤ 2.37) = 0.9910

(b) P(1.14 < z < 3.35) = P(z < 3.35) - P(z < 1.14) = 0.9992 - 0.8708 = 0.1284

(c) P(-0.77 ≤ z ≤ -0.56) = P(z ≤ -0.56) - P(z < -0.77) = 0.2868 - 0.2224 = 0.0644

(d) P(z ≥ -3.28) = 1 - P(z < -3.28) = 1 - 0.0005 = 0.9995

Therefore,

P(z ≤ 2.37) = 0.9910,

P(1.14 < z < 3.35) = 0.1284,

P(-0.77≤ z ≤-0.56) = 0.0644,

P(z≥ -3.28) = 0.9995.