The Standard Normal Distribution

Question

For a standard normal distribution, find:

P(-1.01 < z < 1.31)

Answer 1

Hi Marcella,

Since the normal distribution table tells us the Pr (Z ≤ z) in order to find the probability z is between two values we find the probability z is less than the bigger value and we minus it from the probability z is less than the smaller value.

To find the Pr(-1.01 ≤ z ≤ 1.31) we find the Pr(z ≤ 1.31) - Pr(z ≤ -1.01) .

Thiis is φ(1.31) -φ(-1.01) ≈ 0.90490 - 0.15625 ≈ 0.74865

Once again

Pr(-1.01 ≤ z ≤ 1.31)

= Pr(z ≤ 1.31) - Pr(z ≤ -1.01)

= φ(1.31) -φ(-1.01) ≈ 0.90490 - 0.15625 ≈ 0.74865