Question

A normal distribution has a mean of 10 and a standard deviation of 1. What is the probability of selecting a number between 8 and 12?

Leave the answer in decimal form to 3 decimal places

Answer 1

95.44%

Explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 8 we have:

z = (8 - 10) / (1)

z = -2

and this value represents 0.0228

for 12 we have:

z = (12 - 10) / (1)

z = 2

and this value represents 0.9772

we subtract:

0.9772 - 0.0228 = 0.9544

Which means that it represents 95.44%