Question

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?

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?

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?

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...

The shape of the distribution
of the time required to get an oil change at a
10
-minute
oil-change facility is
unknown. However, records indicate that the mean time
is
11.6
minutes
,
and the standard deviation
is
4.3
minutes
What is the probability that a random sample of n =35 oil
changes results in a sample mean time less than 10 minutes?

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 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 shape of the distribution of the time required to get an oil
change at a
1515 -minute
oil-change facility is unknown. However, records indicate that
the mean time is
16.6 minutes
and the standard deviation is
3.6 minutes
Complete parts (a) through (c) below.
What is the probability that a random sample of
nequals=35
oil changes results in a sample mean time less than
15
minutes?
Suppose the manager agrees to pay each employee a $50 bonus if
they...

The shape of the distribution of the time required to get an oil
change at a 10-Minute oil-change facility is unknown. However,
records indicate that the mean time is 11.2 minutes, and the
standard deviation is 4.9 minutes.
What is the probability that a random sample of n=35 oil changes
results in a sample mean time less than 10 minutes? Please answer
rounding to four decimal places.

The shape of the distribution of the time is required to get an
oil change at a 15-minute oil-change facility is unknown. However,
records indicate that the mean time is 16.2 minutes, and the
standard deviation is 4.2 minutes. Complete parts (a) through
(c).
(a) To compute probabilities regarding the sample mean using the
normal model, what size sample would be required?
A. The sample size needs to be less than or equal to 30.
B. The sample size needs...

The shape of the distribution of the time required to get an
oil change at a 20-minute oil-change facility is unknown.
However, records indicate that the mean time is 21.7 minutes, and
the standard deviation is 4.6 minutes.
(a) To compute probabilities regarding the sample mean using
the normal model, what size sample would be required?
(b) What is the probability that a random sample of nequals35
oil changes results in a sample mean time less than 20
minutes?

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