Algebra 2 Question help!?

Question

I'm given the horizontal table:

Titled Probablity of Specific Processing Times (in seconds)

Processing time, t: 10,20,30,40,50,60

Probability, P(t): 0.052, 0.132, 0.158, 0.135, 0.123, 0.104

Processing time, t: 70,80,90,100,110,120

Probability, P(t): 0.058, 0.034, 0.116, 0.050, 0.026, 0.012

And then told:

Perform a simulation for 50 customers who arrive at the ticket booth. To do so, use the random-number generator of your graphing calculator to generate 50 numbers between 1 and 1000 inclusive. Make a table like the one shown by recording the random numbers in the Number column and the corresponding value of t in the Time column. (For example, if the first random number generated is 174, then the corresponding value of t is 20. This simulates a processing time of 20 seconds for the first customer.)

And given the vertical graph. Each --- is a different column. I tried to make it look how it looks on my paper:

Customer --- Number, N --- Time,t

1

2

:

50

I don't know where to begin thanks so much for any help

Answer 1

The reason it asks you to make random numbers up to 1000 is because the probabilities are listed in thousandths (that is, to three digits past the decimal).  The idea is that the first 52 of the 1000 possible outcomes correspond to t=10, because the probability for t=10 is 0.052.  See, out of a thousand trials, 52 of them should end up with the result t=10...giving it a probability of 52/1000 = .052.

The next 132 outcomes (that is, outcomes 53 through 184) correspond to t=20.  This is why the random number 174 corresponds to t=20: it's between 53 and 184.

The next 158 outcomes (that is, 185 through 342) correspond to t=30.

Do you see where I'm getting my numbers?  If not, look back at your table of probabilities but ignore the decimal points.

If I was doing this, I'd write a program on the calculator, which would store a random number in a variable, and then do the calculations.  (If you use a phrase like "rand(1000)" more than once, the program will probably generate a new random number for each call.)