Question

What is the probability that a value falls in the interval μ ± 2σ, that computes the probability P(-2 < Z < 2). Round to four decimals and use leading zeros

Answer 1

0.9544

Explanation:

P(-2 < Z < 2) means that Z has mean 0 and standard deviation 2.

P(−2 < Z < 2) = F(2) - F(-2)

Using the Z - table,

F(2) = 0.9772

and F(-2) = 0.0228

Thus,

P(−2 < Z < 2) = 0.9772 - 0.0228 = 0.9544

This means that data within two standard deviation is 95%.