Question

1. Assume the waiting time at the BMV is uniformly distributed from 10 to 60 minutes, i.e. X ∼ U ( 10 , 60 )X ∼ U ( 10 , 60 )

What is the expected time waited (mean), and standard deviation for the above uniform variable?

1B) What is the probability that a person at the BMV waits longer than 45 minutes?

1C) What is the probability that an individual waits between 15 and 20 minutes, OR 35 and 40 minutes, i.e. P ( 15 ≤ X ≤ 20 ∪ 35 ≤ X ≤ 40 )?

Answer #1

a)

Here, the given values of lower limit, a = 10 and upper limit, b =
60

For Uniform distribution,

Mean = (a + b)/2

Mean = (10 + 60)/2 = 35

Standard Deviation = sqrt((b - a)^2/12)

Standard Deviation = sqrt((60 - 10)^2/12 = 14.4338

b)

Here, the given values of lower limit, a = 10 and upper limit, b = 60

For Uniform Distribution,

P(X >= x) = (b - x)/(b - a)

P(X >= 45) = (45 - 10)/(60 - 10)

P(X >= 45) = 0.3

c)

Here, the given values of lower limit, a = 10 and upper limit, b = 60

For Uniform Distribution,

P(x1 <= X <= x2) = (x2 - x1)/(b - a)

P(15 <= X <= 20) = (20 - 15)/(60 - 10)

P(15 <= X <= 20) = 0.1

Here, the given values of lower limit, a = 10 and upper limit, b = 60

For Uniform Distribution,

P(x1 <= X <= x2) = (x2 - x1)/(b - a)

P(35 <= X <= 40) = (40 - 35)/(60 - 10)

P(35 <= X <= 40) = 0.1

. P ( 15 ≤ X ≤ 20 ∪ 35 ≤ X ≤ 40 ) = 0.1 + 0.1 = 0.2

The amount of time, in minutes, that a person must wait for a
taxi is uniformly distributed between 1 and 30 minutes,
inclusive.
1.Find the probability density function, f(x).
2.Find the mean.
3.Find the standard deviation.
4.What is the probability that a person waits fewer than 5
minutes.
5.What is the probability that a person waits more than 21
minutes.
6.What is the probability that a person waits exactly 5
minutes.
7.What is the probability that a person waits between...

assume that the amount of time (x), in minutes that a person must
wait for a bus is uniformly distributed between 0 & 20 min.
a) find the mathematical expression for the probability
distribution and draw a diagram. assume that the waiting time is
randomly selected from the above interval
b) find the probability that a eprson wait elss than 15
min.
c) find the probability that a person waits between 5-10
min.
d) find the probability the waiting time...

The expected waiting time at the DMV is 25 minutes, and is
exponentially distributed. If you have already waited for 15
minutes, how much longer should you expect to wait?

A server whose service time is uniformly distributed with an
interval of (10, 20) minutes. The customer inter-arrival time is
also uniformly distributed with an internal (15, 25) minutes.
Determine the expected waiting time of customers of the
queue?

The amount of time, in minutes, that a person must wait
for a bus is uniformly distributed between 0 and 15 minutes,
inclusive.
1. What is the average time a person must wait for a
bus?
2. What is the probability that a person waits 12.5
minutes or less?

The amount of time, in minutes, that a person must wait for a
bus is uniformly distributed between zero and 20 minutes,
inclusive.
What is the probability that a person waits fewer than 13.5
minutes?
On the average, how long must a person wait? Find the mean, μ,
and the standard deviation, σ.
Find the 40th percentile. Draw a graph.

Suppose that the average waiting time at a banking service is 10
minutes. A customer waited for 10 minutes, find the probability
that he will be still waiting after 30 minutes. What is the
approximate probability that the average waiting time of the next
25 customers is at most 12 minutes?

Suppose that the average waiting time at a banking service is 10
minutes.
A customer waited for 10 minutes, find the probability that he
will be still waiting after 30 minutes.
What is the approximate probability that the average waiting
time of the next 25 customers is at most 12 minutes?

The waiting time at a certain checkout counter follows an
exponential distribution with a mean waiting time of five
minutes.
a) Compute the probability that an individual customer waits
longer than 5 1/2 minutes at the checkout counter.
b) Compute the exact probability that the average checkout time
for 5 individuals is greater than 5 ½ minutes.
c) Compute the exact probability that the average checkout time
for 15 individuals is greater than 5 ½ minutes.
d) Apply the Central...

The number of minutes that a patient waits at a medical clinic
to see a doctor is represented by a uniform distribution between
zero and 30 minutes, inclusive.
a. If X equals the number of minutes a person waits, what is the
distribution of X?
b. Write the probability density function for this
distribution.
c. What is the mean and standard deviation for waiting time?
d. What is the probability that a patient waits less than ten
minutes?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 36 minutes ago

asked 36 minutes ago

asked 42 minutes ago

asked 46 minutes ago

asked 53 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago