Question

The length of a text messaging conversation is normally distributed with a mean of 2 minutes and a standard deviation of 0.5 minutes. What is the probability that a conversation lasts longer than 3 minutes? 0.043351 0.063748 0.02275 0.095424

Answer 1

Given:
μ = 2 min, population mean
σ = 0.5 min, population standard deviation

We want to find P(x>3).

Calculate the z-score
 z= (x-μ)/σ = (3-2)/0.5 = 2

From standard tables, obtain
P(x ≤ 3) = P(z ≤ 2) = 0.9772
Therefore
P(x > 3) = P(z > 2) = 1 - 0.9772 = 0.0228

Answer: 0.02275