The number of customers entering a 24-hour convenience store every 10-minutes can be modeled by the Poisson distribution with a a mean of λ=5.4 customers. You are to look at the amount of time passing between successive customers entering the convenience store, represented by X. (a) How many minutes can you expect to pass between successive customers entering the convenience store? (use at least two decimals in your answer) (b) Compute the probability at most 1 minutes will pass between the arrival of one customer and the next customer. In answering this question, be sure to use your answer in (a) to two decimals. Enter your answer using four decimals, and, if necessary, use your answer in part (a). P(X≤1)=_______ (c) Find the probability that at least 1.75 to at most 3.25 minutes pass between the entry of two customers in the store. Use four decimals in your answer. P(1.75≤X≤3.25)= _________ (d) At least 1 minute has passed since the last customer entered the store. What is the probability that in total, at least 2.5 minutes will pass until the next customer enters this store? Use four decimals in your answer. (use four decimals in your answer)
The number of customers entering a 24-hour convenience store every 10-minutes can be modeled by the Poisson distribution with a a mean of λ=5.4 customers. You are to look at the amount of time passing between successive customers entering the convenience store, represented by X.
(a) How many minutes can you expect to pass between successive customers entering the convenience store? (use at least two decimals in your answer)
(b) Compute the probability at most 1 minutes will pass between the arrival of one customer and the next customer. In answering this question, be sure to use your answer in (a) to two decimals. Enter your answer using four decimals, and, if necessary, use your answer in part (a).
P(X≤1)=_______
(c) Find the probability that at least 1.75 to at most 3.25 minutes pass between the entry of two customers in the store. Use four decimals in your answer.
P(1.75≤X≤3.25)= _________
(d) At least 1 minute has passed since the last customer entered the store. What is the probability that in total, at least 2.5 minutes will pass until the next customer enters this store? Use four decimals in your answer.
(use four decimals in your answer)
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