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?

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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?

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It is given that Roanoke college student spends on Instagram has an approximately exponential distribution with a mean μof 60 students. 

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

Therefore, 

X~exponentialλSince, λ=1μ=160X~exponential160

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

fx=160e-x60 , x>0

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