Population standard deviation, critical z-value and normal tables

CFA Level I Quant
#1

A population is normally distributed with a given expected future value and standard deviation.

The probability that the population will be at least 2 standard deviations away from its mean is 0.0456.

I don’t understand how we get 0.0456 from the normal table where the critical z-value is 2.00.

#2

If you look at a Z-table which gives the cumulative probability from -∞ to +2.00, the value is 0.9772. Thus, the probability of being more than 2 standard deviations _ above _ the mean is 1 – 0.9772 = 0.0228. Because the normal distribution is symmetric about the mean, the probability of being more than 2 standard deviations _ below _ the mean is also 0.0228. Thus, the probability of being at least 2 standard deviations away from the mean (either above it or below it) is 0.0228 + 0.0228 = 0.0456.

#3

Ah, it’s all clear now.

Thanks S2000magician!

#4

Good to hear.

You’re welcome.