Review Quiz (Quantitative Methods/Statistics)

8 Problems in Quantitative Methods/Statistics

Covered information is related to simulation, probability, standard deviation, etc... Need to have the solutions to the review quiz (which is UNGRADED) provided in full with each step outlined (in other words, I need to see the work behind the answer).

(See attached file for full problem description)

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3. The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Minutes Relative Frequency
3 0.22
4 0.36
5 0.28
6 0.10
7 0.04
Using these random numbers, simulate the drying time for 5 processes: 0.13; 0.09; 0.19; 0.81; and 0.12.

4. Demand Frequency Random Numbers: 62 13 25 40
0 0.15
1 0.30
2 0.25
3 0.15
4 0.15
If a simulation begins with the first random number, what would the first simulation value be?

5. Demand Frequency Random Numbers: 62 13 25 40
5 0.15
6 0.30
7 0.25
8 0.15
9 0.15
Determine the random number ranges for the above data set (Start with 00).

8. The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Minutes Relative Frequency
3 0.22
4 0.36
5 0.28
6 0.10
7 0.04
Compute the mean drying time.

9. A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate 2 values from this distribution, and has drawn these random numbers: -0.6 and 1.4. What are the 2 values respectively?

10. The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Number of cars arriving Frequency
3 or less 0
4 10
10 30
6 70
7 50
8 40
9 or more 0

Determine the probability distribution of car arrivals.

11. The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Number of cars arriving Frequency
3 or less 0
4 10
11 30
6 70
7 50
8 40
9 or more 0
Based on the above frequencies, two digit random numbers are used and the following random number ranges have been developed.

Number of cars arriving Random Number ranges
4 00-04
5 05-19
6 20-54
7 55-79

Using the following sequence of random numbers, simulate 6 hours of car arrivals at Joe Kelly's oil change and tune-up facility. Random numbers: 92, 44, 15,77,21,38.

12. George Nanchoff owns a gas station. The cars arrive at the gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution. Using the following random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08, estimate the average customer waiting time , average teller idle time and the average time a car spends in the system.

Interarrival times (in min.) P(X) Random Numbers Service time (in minutes) P (X) Random Numbers
4 .35 00-34 2 .30 00-29
7 .25 35-59 4 .40 30-69
10 .30 60-89 6 .20 70-89
20 .10 90-99 8 .10 90-99
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