Answer to Question #255125 in Statistics and Probability for Zah

Question

The time taken to complete a web-based questionnaire is normally distributed, with an average time (μ) of 9 minutes and a standard deviation (σ) of 1.55 minutes. What is the probability that a randomly selected person will take: Between 8 and 8.5 minutes to complete the questionnaire? Interpret your answer.

Answer 1

We have the normal distribution $N(9, 1.55^{2}) = 9 + 1.55N(0,1)$

The goal is to find $P(8< 9 + 1.55N(0,1)<8.5) = P(-0.65<N(0,1)<-0.32) =$

$= P(N(0,1) < -0.32) - P(N(0,1)<-0.65)= 0.37448 - 0.25785 = 0.11663$