Attach a copy of your excel worksheet. At the end/bottom of each excel sheet wri

Question

Attach a copy of your excel worksheet. At the end/bottom of each excel sheet write down the (excel) equation you used to generate each column of data, and your final answers. Write your name on the answer sheets and make sure what you submit is clean and readable. Tossing a coin Simulate Tossing a coin 30 times and answer these questions: Possible outcomes are: Sample space, S = Experimental Probability of getting "Tail" Theoretical Probability of getting "Tail" Picking a card. In this experiment, a card is picked from a stack of six cards, which spell the word PASCAL. (Each letter is written on one card). Simulate the experiment and answer the following questions: Possible outcomes are: Sample space, S = Experimental Probability of getting "A" Theoretical Probability of getting "A" Suppose the ABC trucking Company delivers raw material to your factory. Each truck carries about 18 tons of raw material. The time between subsequent arrivals of trucks is random and changes between 30 to 75 minutes. Let us assume that the first truck always arrives at 8: 00 AM. Simulate the delivery operation for one day (8 hours /day) and determine how many tons of raw material is delivered in a day. What time (clock time) the last truck will arrive? Repeat the simulation in question 1 (above) 5 times and from the output data, determine Maximum, Minimum, and average tons of raw material delivered per day. From the 5 trials in question 2, determine Average number of trucks (arriving) per day

Explanation / Answer

Experiment 1

1) Possible outcomes are either head or tail.

2), Sample space S is determined by 2^30 which would be 1073741824 which is very big.

Let us fix a convention,

0= tail

1= head

On flipping a coin 30 times we will get,

0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1

Number of times Head come = 16

Number of times tail come= 14

Theoretical probability of getting "Tail"

= Number of times tail appeared/ Total Number of trials

= 14/30= 0.466

Experimental Probability of getting a "Tail"

= Number of possible outcomes/ total number of outcomes

= 14/30= 0.466

Theoretical probability is equal to Experimental Probability

Experiment 2 Picking a card from a stack of six cards

1) Possible outcomes are P, A1, S, C, A2, and L

2 Sample space S ={ P, A1, S, C, A2, L}. There are two cards with letter A

Experimental Probability of getting A

= number of outcomes/ total number of outcomes

= 2/6= 1/3

Theoretical probability of getting A

= Number of favourable cases/ total number of cases

= 2/6= 1/3

Experiment 3) ABC trucking

1) The time between subsequent arrival of truck is random and varies between 30 to 75 minutes. First truck always arrive at 8:00am . Here we will simulate it for one day (8hours/day). So the work must be finished by 4:00pm

First truck arrival timing is 8:00 am second is 8:45 third is 9:15, 9:55 , 10:40, 11:40, 12:55, 1:25, 2:15, 2:45, 3:30, 4:00

Last truck will arrive around at 4:00PM but not take above 4:00PM. If time changes in above format.

12 trucks delivered raw material. Each truck carried around 18 ton raw material. Then 12 trucks will deliver around 12*18= 216 tonnes raw material

Note : question 2 and 3 of experiment 3 will be done on excel by using simulation formula.

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