Problem 2. (10 points) The amount of time passing between successive customer "check-ins" to a downtown Calgary hotel can be modeled by the Exponential distribution with a mean of 15 minutes. (a) What can you say about the distribution of the time passing between the successive 'check-ins' of customers at this downtown Calgary hotel? ○ A. The distribution is symmetrical with a mean of 15 minutes and a standard deviation of 15 minutes. ○ B. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 225 minutes². C. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. ○ D. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 225 minutes². ○ E. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. ○ F. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. O G. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. (b) Compute the probability that the amount of time passing between the arrival of successive customers who check-in is (i) less than 8 minutes. (Use four decimals in your answer) (ii) between 9.5 and 19 minutes. (Use four decimals in your answer) (iii) more than 27 minutes. (Use four decimals in your answer) (c) If 10 minutes have passed since the last customer checked-in, what is the probability that at least another 15 minutes will pass until the next customer checks-in to this hotel? (Use four decimals in your answer) (d) The number of minutes passing between successive customer check-ins is at most how many minutes, 95% of the time? minutes (Use two decimals in your answer)
Problem 2. (10 points) The amount of time passing between successive customer "check-ins" to a downtown Calgary hotel can be modeled by the Exponential distribution with a mean of 15 minutes. (a) What can you say about the distribution of the time passing between the successive 'check-ins' of customers at this downtown Calgary hotel? ○ A. The distribution is symmetrical with a mean of 15 minutes and a standard deviation of 15 minutes. ○ B. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 225 minutes². C. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. ○ D. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 225 minutes². ○ E. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. ○ F. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. O G. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. (b) Compute the probability that the amount of time passing between the arrival of successive customers who check-in is (i) less than 8 minutes. (Use four decimals in your answer) (ii) between 9.5 and 19 minutes. (Use four decimals in your answer) (iii) more than 27 minutes. (Use four decimals in your answer) (c) If 10 minutes have passed since the last customer checked-in, what is the probability that at least another 15 minutes will pass until the next customer checks-in to this hotel? (Use four decimals in your answer) (d) The number of minutes passing between successive customer check-ins is at most how many minutes, 95% of the time? minutes (Use two decimals in your answer)
Problem 2. (10 points) The amount of time passing between successive customer "check-ins" to a downtown Calgary hotel can be modeled by the Exponential distribution with a mean of 15 minutes. (a) What can you say about the distribution of the time passing between the successive 'check-ins' of customers at this downtown Calgary hotel? ○ A. The distribution is symmetrical with a mean of 15 minutes and a standard deviation of 15 minutes. ○ B. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 225 minutes². C. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. ○ D. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 225 minutes². ○ E. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. ○ F. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. O G. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. (b) Compute the probability that the amount of time passing between the arrival of successive customers who check-in is (i) less than 8 minutes. (Use four decimals in your answer) (ii) between 9.5 and 19 minutes. (Use four decimals in your answer) (iii) more than 27 minutes. (Use four decimals in your answer) (c) If 10 minutes have passed since the last customer checked-in, what is the probability that at least another 15 minutes will pass until the next customer checks-in to this hotel? (Use four decimals in your answer) (d) The number of minutes passing between successive customer check-ins is at most how many minutes, 95% of the time? minutes (Use two decimals in your answer)
The amount of time passing between successive customer "check-ins" to a downtown Calgary hotel can be modeled by the Exponential distribution with a mean of 15 minutes.
(a) What can you say about the distribution of the time passing between the successive 'check-ins' of customers at this downtown Calgary hotel? A. The distribution is symmetrical with a mean of 15 minutes and a standard deviation of 15 minutes. B. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 225 �������2. C. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. D. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 225 �������2. E. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 15 minutes. F. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes. G. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 15 minutes.
(b) Compute the probability that the amount of time passing between the arrival of successive customers who check-in is
(i) less than 8 minutes. (Use four decimals in your answer)
(ii) between 9.5 and 19 minutes. (Use four decimals in your answer)
(iii) more than 27 minutes. (Use four decimals in your answer)
(c) If 10 minutes have passed since the last customer checked-in, what is the probability that at least another 15 minutes will pass until the next customer checks-in to this hotel?
(Use four decimals in your answer)
(d) The number of minutes passing between successive customer check-ins is at most how many minutes, 95% of the time?
minutes (Use two decimals in your answer)
Transcribed Image Text:Problem 2. (10 points)
The amount of time passing between successive customer "check-ins" to a downtown Calgary hotel can be modeled by the Exponential distribution with a mean of 15 minutes.
(a) What can you say about the distribution of the time passing between the successive 'check-ins' of customers at this downtown Calgary hotel?
○ A. The distribution is symmetrical with a mean of 15 minutes and a standard deviation of 15 minutes.
○ B. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 225 minutes².
C. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes.
○ D. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 225 minutes².
○ E. The distribution is left-skewed with a mean of 15 minutes and a standard deviation of 15 minutes.
○ F. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 3.87 minutes.
O G. The distribution is right-skewed with a mean of 15 minutes and a standard deviation of 15 minutes.
(b) Compute the probability that the amount of time passing between the arrival of successive customers who check-in is
(i) less than 8 minutes. (Use four decimals in your answer)
(ii) between 9.5 and 19 minutes. (Use four decimals in your answer)
(iii) more than 27 minutes. (Use four decimals in your answer)
(c) If 10 minutes have passed since the last customer checked-in, what is the probability that at least another 15 minutes will pass until the next customer checks-in to this hotel?
(Use four decimals in your answer)
(d) The number of minutes passing between successive customer check-ins is at most how many minutes, 95% of the time?
minutes (Use two decimals in your answer)
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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