IT 223: Data Analysis
Assignment 6 Solutions
Proportions
These problems match a binary setting, where you have a set of independent yes/no outcomes. In this case, each error will have a caught or not-caught outcome. There are 50 outcomes (n=50) and the probability of catching an error (p=.8) is 80%.
SD = sqrt(n p (1 - p)) = sqrt(50 * .8 * .2) = 2.83
The cumulative proportion of 1.77 is .962 so the probability of finding more than 45 is 1 - .962, which is .038 (or 3.8%).
SD = sqrt(p (1 - p) / n)) = sqrt(.8 * .2 / n) = .0566
The cumulative proportion for -1.77 is .038. The probability of getting more than this score is 1 - .038, which is .962 (or 96.2%).
Dice Rolling Revisited
2. The variance of one roll can be calculated in one of two ways:
· 1/6 (1 - 3.5)2 + 1/6 (2 - 3.5)2 + 1/6 (3 - 3.5)2 + 1/6 (4 - 3.5)2 + 1/6 (5 - 3.5)2 + 1/6 (6 - 3.5)2
· Taking the population variance (VARP in Excel) of 1, 2, 3, 4, 5, 6
Either method produces a variance of 2.92 The standard deviation is the square-root of the variance, which is 1.71.
The standard error for the sample of 20 is SD of one roll divided by sqrt(n):
1.71 / sqrt(50) = .242