After 8:00pm on each Thursday, the amount of time that a person spends waiting in line to get into a well-known pub is a random variable represented by X. Suppose we can model the behavior of ✗ with the exponential probability distribution with an average waiting time of 42 minutes. (a) Provide the standard deviation of this distribution. SD(X) -☐ minutes (b) Suppose you are in line to get into the pub. Compute the probability that you will have to wait between 29 and 36 minutes to get in. Answer with four decimals. P(29≤ X ≤36) (c) It has been at least 30 minutes since you entered the lineup to get into the pub, and you are still waiting. What is the chance that you will have to wait at most 60 minutes in total? Use four decimals in your answer. P(wait in total at most 60 minutes) (d) 55% of the time, you will have to wait at most how many minutes to get into this pub? Enter your answer to two decimals. minutes

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After 8:00pm on each Thursday, the amount of time that a person spends waiting in line to get into a well-known pub is a random variable represented by �. Suppose we can model the behavior of � with the exponential probability distribution with an average waiting time of 42 minutes.

(a) Provide the standard deviation of this distribution.

��(�)=  minutes

(b) Suppose you are in line to get into the pub. Compute the probability that you will have to wait between 29 and 36 minutes to get in. Answer with four decimals.

�(29≤�≤36)=

(c) It has been at least 30 minutes since you entered the lineup to get into the pub, and you are still waiting. What is the chance that you will have to wait at most 60 minutes in total? Use four decimals in your answer.

�(�����������������60�������)= 

(d) 55% of the time, you will have to wait at most how many minutes to get into this pub? Enter your answer to two decimals.

 minutes

After 8:00pm on each Thursday, the amount of time that a person spends waiting in line to get into a well-known pub is a random variable represented by X. Suppose we can
model the behavior of ✗ with the exponential probability distribution with an average waiting time of 42 minutes.
(a) Provide the standard deviation of this distribution.
SD(X)
-☐ minutes
(b) Suppose you are in line to get into the pub. Compute the probability that you will have to wait between 29 and 36 minutes to get in. Answer with four decimals.
P(29≤ X ≤36)
(c) It has been at least 30 minutes since you entered the lineup to get into the pub, and you are still waiting. What is the chance that you will have to wait at most 60 minutes in
total? Use four decimals in your answer.
P(wait in total at most 60 minutes)
(d) 55% of the time, you will have to wait at most how many minutes to get into this pub? Enter your answer to two decimals.
minutes
Transcribed Image Text:After 8:00pm on each Thursday, the amount of time that a person spends waiting in line to get into a well-known pub is a random variable represented by X. Suppose we can model the behavior of ✗ with the exponential probability distribution with an average waiting time of 42 minutes. (a) Provide the standard deviation of this distribution. SD(X) -☐ minutes (b) Suppose you are in line to get into the pub. Compute the probability that you will have to wait between 29 and 36 minutes to get in. Answer with four decimals. P(29≤ X ≤36) (c) It has been at least 30 minutes since you entered the lineup to get into the pub, and you are still waiting. What is the chance that you will have to wait at most 60 minutes in total? Use four decimals in your answer. P(wait in total at most 60 minutes) (d) 55% of the time, you will have to wait at most how many minutes to get into this pub? Enter your answer to two decimals. minutes
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