Enter the value of p so the expression 5/6 - 1/3n is equivalent to p(5 - 2n).
1 answer:
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Answer:
a) 0.125
b) 7
c) 0.875 hr
d) 1 hr
e) 0.875
Step-by-step explanation:l
Given:
Arrival rate, λ = 7
Service rate, μ = 8
a) probability that no requests for assistance are in the system (system is idle).
Let's first find p.
a) ρ = λ/μ
Probability that the system is idle =
1 - p
= 1 - 0.875
=0.125
probability that no requests for assistance are in the system is 0.125
b) average number of requests that will be waiting for service will be given as:
λ/(μ - λ)
= 7
(c) Average time in minutes before service
= λ/[μ(μ - λ)]
= 0.875 hour
(d) average time at the reference desk in minutes.
Average time in the system js given as: 1/(μ - λ)
= 1 hour
(e) Probability that a new arrival has to wait for service will be:
λ/μ =
= 0.875
We have been given that Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Also, she donates $2 to clean water projects per tax return she files.
Further we know that Sterre charged $7,245 and made a donation of $1,242 this year for the tax returns she filed.
Let x be the number of free income tax returns and y be the number of $35 income tax returns.
Therefore, we can set up:
Since she donates $2 for each return that she files, therefore, we can set up:
Therefore,
Sterre filed 414 tax returns for free and filed 207 tax returns for $35.