Question 1

SCENARIO 6-7
The interval between consecutive hits at a web site is assumed to follow an exponential distribution
with a mean of 40 hits per minute.
-Referring to Scenario 6-7, what is the mean time between consecutive hits?

Accepted Answer

The answer of SCENARIO 6-7
The interval between consecutive hits at...

Question 2

The interval between patients arriving at an outpatient clinic follows 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?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 3

To determine the probability of getting no more than 3 events of interest in a
binomial distribution, you will find the area under the normal curve for X = 2.5 and below.

Accepted Answer

The answer of To determine the probability of getting no...

Question 4

To determine the probability of getting between 2 and 4 events of interest in a
binomial distribution, you will find the area under the normal curve between X = 1.5 and 4.5.

Accepted Answer

The answer of To determine the probability of getting between...

Question 5

The interval between patients arriving at an outpatient clinic follows 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?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 6

One of the reasons that a correction for continuity adjustment is needed when
approximating the binomial distribution with a normal distribution is because a random variable
having a binomial distribution can have only a specified value while a random variable having a
normal distribution can take on any values within an interval around that specified value.

Accepted Answer

This statement is true. The binomial distribution is a discrete distribution, meaning that the random variable can only take on specific integer values. In contrast, the normal distribution is a continuous distribution, meaning that the random variable can take on any values within a range of possible values. This difference in the type of distribution is a key reason why a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution.

Question 7

The interval between patients arriving at an outpatient clinic follows 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

The answer of The interval between patients arriving at an...

Question 8

SCENARIO 6-7
The interval between consecutive hits at a web site is assumed to follow an exponential distribution
with a mean of 40 hits per minute.
-Referring to Scenario 6-7, what is the probability that the next hit at the web site will occur within
10 seconds after just being hit by a visitor?

Accepted Answer

The answer of SCENARIO 6-7
The interval between consecutive hits at...

Question 9

To determine the probability of getting more than 3 events of interest in a binomial
distribution, you will find the area under the normal curve for X = 3.5 and above.

Accepted Answer

This is true because to find the probability of getting more than 3 events of interest in a binomial distribution, we can use the normal approximation to the binomial distribution and calculate the area under the normal curve for X = 3.5 and above.

Question 10

The interval between patients arriving at an outpatient clinic follows 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?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 11

To determine the probability of getting fewer than 3 events of interest in a
binomial distribution, you will find the area under the normal curve for X = 3.5 and below.

Accepted Answer

The answer of To determine the probability of getting fewer...

Question 12

To determine the probability of getting at least 3 events of interest in a binomial
distribution, you will find the area under the normal curve for X = 2.5 and above.

Accepted Answer

False, since the probability of getting at least 3 events of interest in a binomial distribution can be found by summing the individual probabilities for 3, 4, 5, ..., up to the maximum possible number of events. This does not involve finding the area under the normal curve for X = 2.5 and above, which would only be applicable if we were using a normal approximation to the binomial distribution.

Question 13

The interval between patients arriving at an outpatient clinic follows 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

The answer of The interval between patients arriving at an...

Question 14

The interval between patients arriving at an outpatient clinic follows 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?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 15

To determine the probability of getting between 3 and 4 events of interest in a
binomial distribution, you will find the area under the normal curve between X = 3.5 and 4.5.

Accepted Answer

The answer of To determine the probability of getting between...

Question 16

One of the reasons that a correction for continuity adjustment is needed when
approximating the binomial distribution with a normal distribution is because the normal
distribution is used for a discrete random variable while the binomial distribution is used for a
continuous random variable.

Accepted Answer

This statement is incorrect. The binomial distribution and the normal distribution are both used for discrete random variables. The reason that a correction for continuity adjustment is needed is because the binomial distribution is a discrete distribution that takes on integer values, whereas the normal distribution is a continuous distribution that takes on any real value. The continuity correction adjusts for the discrepancy between the discrete and continuous nature of the two distributions.

Question 17

One of the reasons that a correction for continuity adjustment is needed when
approximating the binomial distribution with a normal distribution is because the probability of
getting a specific value of a random variable is zero with the normal distribution.

Accepted Answer

The statement is true. The normal distribution is a continuous distribution, meaning that the probability of getting a specific value of a random variable is zero. However, with the binomial distribution, the probability of getting a specific number of successes is non-zero, making a correction for continuity necessary when approximating with a normal distribution.

Question 18

The interval between patients arriving at an outpatient clinic follows 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?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 19

SCENARIO 6-7
The interval between consecutive hits at a web site is assumed to follow an exponential distribution
with a mean of 40 hits per minute.
-Referring to Scenario 6-7, 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 SCENARIO 6-7
The interval between consecutive hits at...

Question 20

SCENARIO 6-7
The interval between consecutive hits at a web site is assumed to follow an exponential distribution
with a mean of 40 hits per minute.
-Referring to Scenario 6-7, what is the probability that the next hit at the web site will occur
between the next 1.2 and 1.5 seconds after just being hit by a visitor?

Accepted Answer

The answer of SCENARIO 6-7
The interval between consecutive hits at...

Quiz 20: Probability and Combinatorics

SCENARIO 6-7 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with a mean of 40 hits per minute. -Referring to Scenario 6-7, what is the mean time between consecutive hits?

The interval between patients arriving at an outpatient clinic follows 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?

To determine the probability of getting no more than 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 2.5 and below.

To determine the probability of getting between 2 and 4 events of interest in a binomial distribution, you will find the area under the normal curve between X = 1.5 and 4.5.

The interval between patients arriving at an outpatient clinic follows 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?

The interval between patients arriving at an outpatient clinic follows 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?

SCENARIO 6-7 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with a mean of 40 hits per minute. -Referring to Scenario 6-7, what is the probability that the next hit at the web site will occur within 10 seconds after just being hit by a visitor?

To determine the probability of getting more than 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 3.5 and above.

The interval between patients arriving at an outpatient clinic follows 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?

To determine the probability of getting fewer than 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 3.5 and below.

To determine the probability of getting at least 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 2.5 and above.

The interval between patients arriving at an outpatient clinic follows 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?

The interval between patients arriving at an outpatient clinic follows 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?

To determine the probability of getting between 3 and 4 events of interest in a binomial distribution, you will find the area under the normal curve between X = 3.5 and 4.5.

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the normal distribution is used for a discrete random variable while the binomial distribution is used for a continuous random variable.

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the probability of getting a specific value of a random variable is zero with the normal distribution.

The interval between patients arriving at an outpatient clinic follows 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?