A5 P1

Suppose that \(X\), the time between sent text messages for Canadian teenagers, follows an exponential distribution with rate \(\lambda = \frac{1}{ {{params.mu}} }\). Suppose we ask Stacy (a Canadian teenager) to record the next \({{params.size}}\) times between sent text messages and take the average.

Part 1

What distribution does \(\overline{X}\), the sample mean time in minutes between text messages, follow? Please note that we are parameterizing the Normal distribution using the standard deviation, i.e. of the form \(N(\mu, \sigma)\)

Answer Section

• \(Exponential(\lambda = 1/16)\)

• \(Standard\ Normal\), i.e. \(N(0,1)\)

• \(Normal(16, 16)\)

• \(Normal(1/16, 1/16)\)

• \(Normal(16, 16/\sqrt{50})\)

Part 2

What is the probability that the average sample mean time exceeds \({{params.exceed}}\) minutes?

Part 3

What is probability that the total time between the \(1^{st}\) and \( {{ params.endsize }} ^{st}\) text message exceeds \({{ params.totaltime }}\) minutes?

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.