Question

Find the following probabilities based on the standard normal variable Z.

1. a.P(−0.9 ≤ Z ≤ −0.59)b.P(0.04 ≤ Z ≤ 1.72)c.P(−1.4 ≤ Z ≤ 0.06)d.P(Z > 3.6)

Answer 1

We have to use software or Standard Normal table to find its value, I will use R studio here.

R code: pnorm(z)

1)

2)

3)

4)

R Code and output:

> pnorm(-0.59)
[1] 0.2775953
> pnorm(-0.9)
[1] 0.1840601
> pnorm(1.72)
[1] 0.9572838
> pnorm(0.04)
[1] 0.5159534
> pnorm(0.06)-pnorm(-1.4)
[1] 0.4431655
> pnorm(3.6)
[1] 0.9998409