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Market researchers are interested in what convinces people to stay for a long time in a shop. If T is the amount of time a random person spends in the shop, they estimate the probability density function of T to be f(x) = { sin (5x) : 0

Market researchers are interested in what convinces people to stay for a long time in a shop. If T is the amount of time a random person spends in the shop, they estimate the probability density function of T to be f(x) = { sin (5x) : 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 4E
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Market researchers are interested in what convinces people to stay for a long time in a shop. If T is the amount of time a random person spends in the shop, they estimate the probability density function of T to be f(æ) = { sin () : : 0<x< 40 Using the symmetry of f(x), we can find the expected value of T without a long computation: ЕT) — The researchers plan on asking customers for an interview if their stay in the store is more than one standard deviation longer than the expected value of T, or more than one standard deviation shorter. The researchers, therefore, will ask a customer for an interview if the time they spend in the store is greater than or less than Remark: Clicking 'preview my answers' will give you a numerical value for your entry, without using an attempt. Before you submit your answer, think about whether it makes sense in the context of the experiment.
Transcribed Image Text:Market researchers are interested in what convinces people to stay for a long time in a shop. If T is the amount of time a random person spends in the shop, they estimate the probability density function of T to be f(æ) = { sin () : : 0<x< 40 Using the symmetry of f(x), we can find the expected value of T without a long computation: ЕT) — The researchers plan on asking customers for an interview if their stay in the store is more than one standard deviation longer than the expected value of T, or more than one standard deviation shorter. The researchers, therefore, will ask a customer for an interview if the time they spend in the store is greater than or less than Remark: Clicking 'preview my answers' will give you a numerical value for your entry, without using an attempt. Before you submit your answer, think about whether it makes sense in the context of the experiment.
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