In past presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In NYC as well, some voters complained about the long lines in some precincts, with most complaints coming from precinct A. In 2016, the average number of voters arriving at Precinct A was 27 per hour and the arrival of voters was random. Suppose service times were also random and that each voter spent on average 5 minutes in the voting booth (this is the time needed to cast her/his vote using a voting machine). what would be the utilization rate with the minimum number of voting machines to barely satisfy the demand

The utilization rate with the minimum number of voters = 0.75

Step-by-step explanation:

Rate of arrival of voters = 27 voters per hour

If each voter spends 5 minutes in the voting booth,

In 1 hour, number of voters = 60/5 = 12. i.e. service rate = 12 voters per hour

Utilization rate, UR= ...............(1)

Maximum value for UR = 1. i.e UR ≤ 1

number of voters cannot take a decimal value, therefore,

The minimum number of voters = 3

Substituting number of voters into equation (1)

here is me explaining it:

the pizza would be delivered around 5, give or take 15 minutes. this means it could be delivered anywhere from 4: 45 to 5: 15

let's say 5: 00 is equivalent to 0 on a number line and x represents time. 4: 45 would be equal to -15x because we are 15 minutes behind our starting point, 5: 00. 5: 15 would be equal to 15x because we are 15 minutes ahead of your starting point (which means you're late on the pizza delivery! )

absolute value is very confusing. the basic definition is how far you are from your starting point. if we deliver the pizza at 4: 45 (15 minutes before the starting point) we would be -15. this means we are 15 away from our starting point, 5: 00. that's the absolute value. |-15| (absolute value of negative fifteen) is equal to 15. if you did not understand this i suggest rereading this paragraph.

the normal way you would write this scenario would be 4.75 (4 and 3 quarters, or 4: 45. you can also write as a fraction.) is less than x and x is less than 5.25 (5 and 1 quarter or 5: 15). 4.75< x< 5.25 the reason why i am using numbers is because you cannot represent typical time as values on a graph, number line, or in an equation.

another way to write this scenario is with absolute value. we can write this as |x| being less than or equal to .25 (remember, this just means 15 minutes).           |x| ≤ .25.

sorry if the end was confusing. because we are talking about time this whole question is 10x harder. like i said earlier, you cannot represent time as, well, time, in a graph, equation, or number line. i set the values as follows: 1/4 or .25 for 15 minutes, and 1 for 1 hour. this is just a common way to set up graphs involving time.

|x| ≤ .25

i hope this ! : )

tell me if you need more assistance