113. Exponential Probability Between 12:00 PM and 1:00 PM. cars arrive at Citibank's drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. F ( t ) = 1 − e − 0.1 t (a) Determine the probability that a car will arrive within 10 minutes of 12:00 PM (that is, before 12:10 PM). (b) Determine the probability that a car will arrive within 40 minutes of 12:00 PM (before 12:40 PM). (c) What value does F approach as t becomes unbounded in the positive direction? (d) Graph F using a graphing utility. (e) Using INTERSECT, determine how many minutes are needed for the probability to reach 50% .
113. Exponential Probability Between 12:00 PM and 1:00 PM. cars arrive at Citibank's drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. F ( t ) = 1 − e − 0.1 t (a) Determine the probability that a car will arrive within 10 minutes of 12:00 PM (that is, before 12:10 PM). (b) Determine the probability that a car will arrive within 40 minutes of 12:00 PM (before 12:40 PM). (c) What value does F approach as t becomes unbounded in the positive direction? (d) Graph F using a graphing utility. (e) Using INTERSECT, determine how many minutes are needed for the probability to reach 50% .
Solution Summary: The author explains the probability that a car will arrive within 10 minutes, and the value that F approaches as t becomes unbounded in positive direction.
113. Exponential Probability Between 12:00 PM and 1:00 PM. cars arrive at Citibank's drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM.
(a) Determine the probability that a car will arrive within 10 minutes of 12:00 PM (that is, before 12:10 PM).
(b) Determine the probability that a car will arrive within 40 minutes of 12:00 PM (before 12:40 PM).
(c) What value does F approach as t becomes unbounded in the positive direction?
(d) Graph F using a graphing utility.
(e) Using INTERSECT, determine how many minutes are needed for the probability to reach
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Suppose that the length of time spent by a student with a professor during office hours in minutes is an exponential r.v. with parameter ?=1/10. This professor only sees students in the office hour one at a time. Thus, if you arrive to the office and there is someone inside, you have to wait.
Consider 5 randomly chosen days in which you visit the professor's office during the office hour period and someone arrives immediately ahead of you. What is the probability that in one of those days you will have to wait between 10 and 20 minutes?
Show that if a random variable has an exponentialdensity with the parameter θ, the probability that it willtake on a value less than −θ · ln(1 − p) is equal to p for 0 Fp < 1.
4.1 #4 One article states that each one-second delay in loading search results has the effect of multiplying the probability that an online customer will make a purchase by 0.90. Let P! denote the probability, as a percentage, that an Amazon customer will make a purchase if the search results require t seconds to load. What is the exponential model that shows percentage probability P as a function of t?
Chapter 5 Solutions
Student's Solutions Manual for Precalculus Enhanced with Graphing Utilites
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