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Math Lab 4

# Math Lab 4 - 5 6 5 4 3 2 1 80 70 60 50 40 30 20 10 Number...

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Andrew Eskander Math 11 Lab Lab 4 1. There were 5 heads in the first experiment, three in the second, three in the third, and four heads in the fourth experiment. 2. The probability of getting no heads in the five tosses is 0.03125. The probability of getting exactly two heads in the five tosses is 0.31250. 3. There were 26 times where there were no heads in the five tosses. There were 328 times where there were exactly two heads. 5 4 3 2 1 0 350 300 250 200 150 100 50 0 Number times Heads Appears Frequency 29 157 281 328 179 26 Histogram of 1000 times 4. In my 1000 simulations, I did not get zero heads as many times as I expected (.026 while expected is .03125), but I got around the number of expected times for two heads, slightly more, in the simulations (.328 while suspected is .31250).

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Unformatted text preview: 5. 6 5 4 3 2 1 80 70 60 50 40 30 20 10 Number Questions Correct Frequency 4 5 10 49 76 74 32 Histogram of 10 question Quiz Number Questions Correct Expected Probability Simulate Probability 0 0.107374 .128 1 0.268435 .296 2 0.301990 .304 3 0.201327 .196 4 0.088080 .04 5 0.026424 .02 6 0.005505 .016 7 0.000786 8 0.000074 9 0.000004 10 0.000000 The simulation results compare pretty well with the expectations as most of the probabilities determined from the simulation are very comparable to the expected probability. Although not perfect, the probabilities of the expected and simulated are very similar and close. 6. The maximum number of questions any student got correct was 6....
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