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Answer :
The provided data seems to have inconsistencies, making it challenging to provide accurate calculations for some of the given questions. Accurate values for the standard deviation and more specific information would be needed for precise calculations.
In this scenario, you have drawn 100 samples with replacement from a box. The provided data indicates that you drew 17 samples of 54 and 20 samples of 0.
a. The standard deviation (SD) measures the dispersion of values around the mean. To calculate it, you would first find the mean of the draws, which in this case is (17 * 54 + 20 * 0) / 100 = 9.38 (rounded). Then, calculate the squared differences between each draw and the mean, sum them up, divide by the number of draws, and take the square root.
However, it seems there might be a typo or misunderstanding in the provided data because 54 and 0 have a significant difference, and such a scenario might require more detailed information to accurately compute the SD.
b. The expected value (EV) of the sum of draws can be calculated as the sum of each value multiplied by its probability. Given the data, the EV would be 17 * 54 + 20 * 0 = 918 (rounded).
c. The standard error (SE) of the sum of draws represents the uncertainty in the sample mean's estimate. It's calculated by dividing the standard deviation by the square root of the number of samples. However, without accurate standard deviation information, this calculation is not possible.
d. The Z-score for the observed sum of draws indicates how many standard deviations the observed sum is away from the mean. To calculate it, you would subtract the mean (expected sum) from the observed sum and then divide by the standard deviation. However, since accurate SD information is missing, this calculation cannot be performed.
e. The standard error (SE) for the number of 's' (zeros) can be calculated by taking the square root of the product of the probability of getting a '0' and the probability of getting a '1'. Assuming '1' represents all values other than '0', the probability of getting a '0' is 20/100 and the probability of getting a '1' is 80/100. So, the SE for the number of 's' is √(0.2 * 0.8) ≈ 0.4 (rounded to one decimal).
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