Question

Find the probability of each of the following if Z ~ N(μ = 0, σ = 1). (Please round any numerical answers to 4 decimal places.)

a) P(Z > 1.5)
b) P(Z < -2)
c) P(-1 < Z < 2)
d) P(Z > -0.5)

Answer 1

To find the probability in each case, calculate the area under the standard normal curve. P(Z > 1.5) ≈ 0.0668, P(Z < -2) ≈ 0.0228, P(-1 < Z < 2) ≈ 0.8186, P(Z > -0.5) ≈ 0.6915.

Step-by-step explanation:

To find the probability in each case, we need to calculate the area under the standard normal curve.

a) To find P(Z > 1.5), we need to find the area to the right of 1.5 on the standard normal curve. Using a z-table or an online calculator, we find P(Z > 1.5) ≈ 0.0668.

b) To find P(Z < -2), we need to find the area to the left of -2 on the standard normal curve. Using a z-table or an online calculator, we find P(Z < -2) ≈ 0.0228.

c) To find P(-1 < Z < 2), we need to find the area between -1 and 2 on the standard normal curve. Using a z-table or an online calculator, we find P(-1 < Z < 2) ≈ 0.8186.

d) To find P(Z > -0.5), we need to find the area to the right of -0.5 on the standard normal curve. Using a z-table or an online calculator, we find P(Z > -0.5) ≈ 0.6915.