Answered: The amount of time a Roanoke College…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The amount of time a Roanoke College student spends on Instagram has an approximately exponential distribution with mean 60 minutes.

a. What is the probability a randomly selected student spends less than 45 on Instagram?

b. Illustrate your answer from a. using the pdf.

c. Find the cumulative distribution function for the time students spend on Instagram.

d. What is the probability a randomly selected student is on Instagram for a time within 2 standard deviation of the mean?

Expert Solution

Step 1

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It is given that Roanoke college student spends on Instagram has an approximately exponential distribution with a mean $(μ)$ of 60 students.

X: The amount of time a student spends on Instagram.

Therefore,

$X ~ e x p o n e n t i a l (λ) S i n c e, λ = \frac{1}{μ} = \frac{1}{60} X ~ e x p o n e n t i a l (\frac{1}{60})$

Thus, the density function of the time that a student spends on Instagram is:

$f (x) = \frac{1}{60} e^{- \frac{x}{60}}, x > 0$

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