Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 13.6; σ = 3.5 P(8 ≤ x ≤ 12) =

Answer 1

Given that x has a normal distribution with the specified mean and standard deviation μ = 13.6; σ = 3.5. To calculate the indicated probability P(8 ≤ x ≤ 12) we need to find the Z score at X = 8 and X = 12 as:

Now the probability is computed as:

Therefore the probability is calculated using the excel formula for normal distribution which is =NORM.S.DIST(-0.4571, TRUE)- NORM.S.DIST(-1.6, TRUE), thus the probability is;

=> 0.3238−0.0548=0.2690