Question

1. Suppose that values are repeatedly chosen from the standard normal
distribution, N(μ = 0, σ = 1).
(1) In the long run, what proportion of values will be at most 2.15 and at
least -0.5?
(2) What is the long-run proportion of selected values that will exceed
-1.23?
(3) What is the 24th percentile of the standard normal distribution?

Answer 1

Here we want to find P(Z <= 2.15) and P( Z >= -0.5)

From Z table

P(Z <= 2.15 ) = 0.9842

and P( X >= -0.5 ) = 1 - P( Z< -0.5) = 1 - 0.3085 = 0.6915

2) Here we want to find P(Z > -1.23) = 1 - P( Z <= -1.23) = 1 - 0.1093 = 0.8907

3) Here we want to find z such that P(Z < z) = 0.24

Find the closest area to 0.2400 in the Z table and then write its corresponding z value.

The most closest area from 0.2400 is 0.2389

It's corresponding z value is -0.71

THerefore answer of this part is -0.71