Question

The time it takes to completely tune an engine of an
automobile follows an exponential distribution with a mean of 48
minutes. (Total: 4 marks; 2 marks each)

a. What is the probability of tuning an engine in 36 minutes
or less?

b. What is the probability of tuning an engine between 24 and
36 minutes?

Answer #1

The time between arrivals at a toll booth follows an
exponential distribution with a mean time between arrivals of 2
minutes.
What is the probability that the time between two successive
arrivals will be less than 3 minutes?
What is the probability that the time will be between 3 and 1
minutes?

1. The process time of oil change in a car follows an
exponential distribution with a mean of 5 minutes. What is the
probability that a process of oil change takes more than 6
minutes?
2. What is the probability that a process of oil change takes
between 3 and 5 minutes?

The
time between telephone calls to a cable televisiom service call
center follows an exponential distribution with a mean of 1.5
minutes.
a. What is the probability that the time between the next two
calls will be 48 seconds or less?
b. What is the probability that the between the next two calls
will be greater than 118.5 seconds?

The waiting time (in minutes) for a new bitcoin block follows an
exponential distribution with? = 15.
a. What is the probability that no blocks are found within 30
minutes?
b. What is the probability that the waiting time for a new block is
between 10 minutes and 20 minutes?
c. What is the probability of finding less than 2 blocks in an
hour?

The time between arrivals of vehicles at a particular
intersection follows an exponential probability distribution with a
mean of 10 seconds. (a) Sketch this exponential probability
distribution.
(b) What is the probability that the arrival time between
vehicles is 10 seconds or less? (Round your answer to four decimal
places.)
(c) What is the probability that the arrival time between
vehicles is 4 seconds or less? (Round your answer to four decimal
places.)
(d) What is the probability of 30...

Suppose that the time between successive occurrences of an event
follows an exponential distribution with mean number of occurrences
per minute given by λ = 5. Assume that an event occurs. (A) Derive
the probability that more than 2 minutes elapses before the
occurrence of the next event. Derive the probability that more than
4 minutes elapses before the occurrence of the next event. (B) Use
to previous results to show: Given that 2 minutes have already
elapsed, what is...

Suppose that the amount of time you spend working on STAT 3600
homework follows an exponential distribution with mean 60 minutes.
a. What is the probability that it takes you less than 50 minutes
to complete the homework? b. Given that you have already spent 40
minutes on the homework and have not finished, what is the
probability that you will spend at least 70 minutes on the
homework?

For a certain soccer team, the time between scoring goals
follows an exponential distribution with a mean of 20 minutes.
Suppose a game starts at 1:00 p.m. Assume the game is played for 90
minutes without breaks.
(a) What is the probability that the team scores no goals during
the Örst 30 minutes?
(b) What is the probability that the team will score its Örst
goal between 30 and 60 minutes?
(c) Suppose that no goals are scored before 2:00...

2. The waiting time between arrivals at a Wendy’s drive-through
follows an exponential distribution with ? = 15 minutes. What is
the distribution of the number of arrivals in an hour?
a. Poisson random variable with μ=15
b. Poisson random variable with μ=4
c. Exponential random variable with ?=15
d. Exponential random variable with ?=4

The time that it takes for the next train to comes follows a
Uniform Distribution with f(x) = 1/10 where x goes between 6 and 16
minutes. Round answers to 4 decimals when possible.
1. Find the probability that the time will be at most 7
minutes.
2. Find the 10th percentile.

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