Question 1

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be less than 10 minutes?

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Question 2

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends between 10 and 15 hours watching TV is ________.

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Question 3

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be more than 5 minutes?

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Question 4

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends more than 5 hours watching TV is ________.

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Question 5

The Townsville International Airport (TIA)has been criticised for the waiting times associated with departing flights.While the critics acknowledge that many flights have little or no waiting times,their complaints deal more specifically with the longer waits attributed to some flights.The critics are interested in showing,mathematically,exactly what the problems are.Which type of distribution would best model the waiting times of the departing flights at TIA?
A)Binomial distribution.
B)Exponential distribution.
C)Uniform distribution.
D)Normal distribution.

Accepted Answer

The exponential distribution is commonly used to model the waiting times for processes that occur randomly over time, such as the arrival of customers at a service desk. It is a continuous probability distribution that has a memoryless property, meaning that the probability of waiting a certain amount of time does not depend on how much time has already elapsed. Therefore, it would be suitable for modeling the waiting times of departing flights at TIA, as each flight's waiting time would be independent of the previous ones.

Question 6

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be between 10 and 15 minutes?

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Question 7

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be less than 15 minutes?

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Question 8

Instruction 6-6
The interval between consecutive hits at a web site is assumed to follow an exponential distribution with an average of 40 hits per minute.
-Referring to Instruction 6-6,what is the probability that the next hit at the web site will occur within 10 seconds after just being hit by a visitor?

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The interval between consecutive hits at...

Question 9

Let X represent the amount of time it takes a student to park in the car park at the university.If we know that the distribution of parking times can be modelled using an exponential distribution with a mean of 4 minutes,find the probability that it will take a randomly selected student more than 10 minutes to park in the car park.
A)0.329680
B)0.670320
C)0.917915
D)0.082085

Accepted Answer

The probability that a randomly selected student will take more than 10 minutes to park can be found using the cumulative distribution function (CDF) of the exponential distribution:

P(X > 10) = 1 - P(X ≤ 10) = 1 - F(10)

where F(10) is the CDF of the exponential distribution with a mean of 4 minutes evaluated at 10 minutes. Using the formula for the CDF of the exponential distribution:

F(x) = 1 - e^(-λx)

where λ is the rate parameter of the distribution (equal to 1/4 in this case), we have:

F(10) = 1 - e^(-10/4) = 0.917915

Therefore,

P(X > 10) = 1 - F(10) = 1 - 0.917915 = 0.082085

So the best choice is D.

Question 10

Let X represent the amount of time it takes a student to park in the car park at the university.If we know that the distribution of parking times can be modelled using an exponential distribution with a mean of 4 minutes,find the probability that it will take a randomly selected student between 2 and 12 minutes to park in the car park.
A)0.656318
B)0.556744
C)0.606531
D)0.049787

Accepted Answer

To solve this problem, we need to use the cumulative distribution function (CDF) of the exponential distribution with a mean of 4 minutes. The CDF is given by F(x) = 1 - e^(-x/4), where x is the parking time.

To find the probability that a student takes between 2 and 12 minutes to park, we need to calculate the difference between the CDF at 12 minutes and the CDF at 2 minutes. So:

P(2 <= X <= 12) = F(12) - F(2)
P(2 <= X <= 12) = (1 - e^(-12/4)) - (1 - e^(-2/4))
P(2 <= X <= 12) = e^(-3) - e^(-1/2)
P(2 <= X <= 12) ≈ 0.556744

Therefore, the best choice is B.

Question 11

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be less than 20 minutes?

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Question 12

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be between 5 minutes and 15 minutes?

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Question 13

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the average number of arrivals per minute?

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Question 14

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends less than 20 hours watching TV is ________.

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Question 15

Instruction 6-6
The interval between consecutive hits at a web site is assumed to follow an exponential distribution with an average of 40 hits per minute.
-Referring to Instruction 6-6,what is the average time between consecutive hits?

Accepted Answer

The answer of Instruction 6-6
The interval between consecutive hits at...

Question 16

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 2.5 hours?

Accepted Answer

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Question 17

Instruction 6-6
The interval between consecutive hits at a web site is assumed to follow an exponential distribution with an average of 40 hits per minute.
-Referring to Instruction 6-6,what is the probability that the next hit at the web site will occur within no sooner than 5 seconds after just being hit by a visitor?

Accepted Answer

The answer of Instruction 6-6
The interval between consecutive hits at...

Question 18

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 1 hour?

Accepted Answer

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Question 19

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be more than 18 minutes?

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Question 20

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be less than 15 minutes?

Accepted Answer

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Quiz 6: The Normal Distribution and Other Continuous Distributions

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be less than 10 minutes?

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends between 10 and 15 hours watching TV is ________.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be more than 5 minutes?

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends more than 5 hours watching TV is ________.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be between 10 and 15 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be less than 15 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be less than 20 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be between 5 minutes and 15 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the average number of arrivals per minute?

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends less than 20 hours watching TV is ________.

Instruction 6-6 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with an average of 40 hits per minute. -Referring to Instruction 6-6,what is the average time between consecutive hits?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 2.5 hours?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 1 hour?

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be more than 18 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be less than 15 minutes?