Question

Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.

Answer 1

For the standard normal distribution Z, the mean μ =0
and σ the standard deviation = 1

a) P(0 ≤ Z ≤ 1.5) →P(Z=1.5) - P(Z=0)
P(0 ≤ Z ≤ 1.5)= 0.9332 - 0.5 = 0.4322

b) P(Z ≥ 2.5) →P(Z=2.5) = 1- P(Z=2.5)
P(Z ≥ 2.5) = 1- 0.9938 = 0.0062

c) P(Z≥ 3.5) = 1-  P(Z =  3.5) = 0
OR  P(Z≤ 3.5) = 0