Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 20 min and variance 80 min (a) What are the values of a and B? a = B = (b) What is the probability that a student uses the terminal for at most 24 min? (Round your answer to three decimal places.) (c) What is the probability that a student spends between 16 and 32 min using the terminal? (Round your answer to three decimal places.)
Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 20 min and variance 80 min (a) What are the values of a and B? a = B = (b) What is the probability that a student uses the terminal for at most 24 min? (Round your answer to three decimal places.) (c) What is the probability that a student spends between 16 and 32 min using the terminal? (Round your answer to three decimal places.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![**Gamma Distribution and Probability Calculation**
Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility follows a gamma distribution with mean \(20\) min and variance \(80\) min\(^2\).
**(a) What are the values of \(\alpha\) and \(\beta\)?**
\[
\alpha = \_\_\_
\]
\[
\beta = \_\_\_
\]
**(b) What is the probability that a student uses the terminal for at most \(24\) min?** (Round your answer to three decimal places.)
**(c) What is the probability that a student spends between \(16\) and \(32\) min using the terminal?** (Round your answer to three decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32f563a-6b55-4123-a4c3-1254c39a7403%2F58dde117-ab36-4a35-9a22-87a92950175a%2Fmfmg3wg_processed.png&w=3840&q=75)
Transcribed Image Text:**Gamma Distribution and Probability Calculation**
Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility follows a gamma distribution with mean \(20\) min and variance \(80\) min\(^2\).
**(a) What are the values of \(\alpha\) and \(\beta\)?**
\[
\alpha = \_\_\_
\]
\[
\beta = \_\_\_
\]
**(b) What is the probability that a student uses the terminal for at most \(24\) min?** (Round your answer to three decimal places.)
**(c) What is the probability that a student spends between \(16\) and \(32\) min using the terminal?** (Round your answer to three decimal places.)
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