Jensen, arriving at a bus stop, just misses the bus. Suppose that he decides to walk if the (next) bus takes longer than 5 minutes to arrive. Suppose also that the time in minutes between the arrivals of buses at the bus stop is a continuous random variable with a U(4, 6) distribution. Let X be the time that Jensen will wait. a. What is the probability that X is less than 4.5 (minutes)? b. What is the probability that X equals 5 (minutes)? Note: A continuous random variable has a uniform distribution on the interval [a, b] if its probability density function fis given by f(x) = 0 if x is not in [a, b] and f(x)=1/(B-a) for a ≤ x ≤ß. We denote this distribution by U(a, B).
Jensen, arriving at a bus stop, just misses the bus. Suppose that he decides to walk if the (next) bus takes longer than 5 minutes to arrive. Suppose also that the time in minutes between the arrivals of buses at the bus stop is a continuous random variable with a U(4, 6) distribution. Let X be the time that Jensen will wait. a. What is the probability that X is less than 4.5 (minutes)? b. What is the probability that X equals 5 (minutes)? Note: A continuous random variable has a uniform distribution on the interval [a, b] if its probability density function fis given by f(x) = 0 if x is not in [a, b] and f(x)=1/(B-a) for a ≤ x ≤ß. We denote this distribution by U(a, B).
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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![Jensen, arriving at a bus stop, just misses the bus. Suppose that he decides to walk if
the (next) bus takes longer than 5 minutes to arrive. Suppose also that the time in
minutes between the arrivals of buses at the bus stop is a continuous random variable
with a U(4, 6) distribution. Let X be the time that Jensen will wait.
a. What is the probability that X is less than 4.5 (minutes)?
b. What is the probability that X equals 5 (minutes)?
Note: A continuous random variable has a uniform distribution on the interval [a, b]
if its probability density function fis given by f(x) = 0 ifx is not in [a, b] and
f(x)=1/(B-a)
for a ≤x≤ß.
We denote this distribution by U(a, ß).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd300c0dc-a0ad-486a-8e3f-43fae65dfe77%2F8f576280-e83e-4843-9a6b-eda3e72b61bf%2F7431otv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Jensen, arriving at a bus stop, just misses the bus. Suppose that he decides to walk if
the (next) bus takes longer than 5 minutes to arrive. Suppose also that the time in
minutes between the arrivals of buses at the bus stop is a continuous random variable
with a U(4, 6) distribution. Let X be the time that Jensen will wait.
a. What is the probability that X is less than 4.5 (minutes)?
b. What is the probability that X equals 5 (minutes)?
Note: A continuous random variable has a uniform distribution on the interval [a, b]
if its probability density function fis given by f(x) = 0 ifx is not in [a, b] and
f(x)=1/(B-a)
for a ≤x≤ß.
We denote this distribution by U(a, ß).
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