Answer:
Arrival rate λ= 19 pages per hour
Service rate μ = 20 pages per hour
a. Average utilization rate <em>P </em>= λ/μ
Average utilization rate <em>P </em>= 19/20
Average utilization rate <em>P </em>= 0.95
Average utilization rate <em>P = </em> 95%
b. Probability that more than four pages are waiting or being word processed Pn>4 = 1 - (<em>P0 + P1 + P2 + P3 + P4)</em>
Pn>4 = 1 - (0.05*(1+0.95 + 0.95^2 + 0.95^3 + 0.95^4))
Pn>4 = 1 - (0.05*4.524)
Pn>4 = 1 - 0.2262
Pn>4 = 0.774.
c. Average number of pages waiting to be word processed <em>Lq</em>
<em>Lq = </em>λ²/μ(μ-λ)
<em>Lq </em>= 19²/20(20-19)
<em>Lq </em>= 361/20
<em>Lq </em>= 18.05
Answer:
a) 55%
b) Joint Probability
c) They are not mutually exclusive
Explanation:
Part 1 of the Question
First, we determine the formula for calculating the probabilities of Yellowstone Park and the Tetons as follows
Probability of Yellow Stone = <em>p(</em>Yellowstone)= 0.5 or 50%
Probability of Tetons = <em>p(</em>Tetons)= 0.4 or 40%
Probability of Both = <em>p(</em>Both)= 0.35 or 35%
Therefore, the probability of visiting at least one by a vacationer is as follows:
p(At least One) = <em>p(</em>Yellowstone or Tetons)
= <em>p(</em>Yellowstone) + <em>p(</em>Tetons) - <em>p(</em>Both)
= 50%+40%-35%
= 0.5+0.4-0.35
= 0.55 or 55%
Part 2 of the Question
First the probability of 35% represents the possibility of a vacationer visiting the two locations, hence, it can be called the percentage of intersection between Tetons and Yellowstone. It is also referred to as joint probability
Part 3 of the Question
Once event are mutually exclusive, it means they cannot be carried out or considered together. In other words, one becomes an alternate cost for the other. This means going to Yellowstone means the vacationer cannot go to Tetons and vice versa. In this situation, the joint probability will not be possible (0%). Since, we already know that there is a joint probability of 35%, it means <u>the events are not mutually excusive</u>
The statement that describes the result is At that price, quantity demanded exceeds quantity supplied. This is because the quantity of the demanded product from the consumer has higher range than the amount of supply from the market. This can results into shortage
<span>The possible journal entry that would be in Truman's tracking inventory would be:
Cash
4,171
Sales discounts
129
Accounts receivable
4,300
This is because the amount of 5,800 had a credit or an excess amount. Originally the costs of the items are 4,000 and it happened to be increased using the 2/10 and n/30 method of the calculation.</span>