A sample statistics test question requires, based on a provided probability distribution of one, two or three adults living per home in a randomly selected neighborhood, determining the probability that four or more adults reside in another randomly selected home. Based on the fact that the total of all the probabilities is one, the answer is determined by adding the probabilities presented and subtracting the sum from one, which in this case was .10, and the correct answer.
A question from a college-level, basic business statistics test describes the tail length of wombats as distributed with a mean of 42 centimeters and a standard deviation of 5 centimeters. The answer, .7257, is the percentage of these wombats with tails 45 centimeters long or shorter. A probability of zero is the answer to a follow-up question as to what percentage of these wombats have tails that are 82 centimeters long or longer.
Another college level question requires the calculation of the sample standard deviation of a group of six numbers: 17.29, 31.44, 29.86,23.42, 19.71 and 27.41. The answer is 5.67. This is followed by a related question that requires using the same data to report, for a normal distribution, what percentage of the data lies within one standard deviation of the mean, 68 percent, and also within two standard deviations of the mean, 95 percent.
A sample advanced placement statistics test question provides the percentage of voters in each of two states who are Republicans and Democrats. The answer requires predicting, from a random sample of 100 voters in each state, which state sample will evidence a greater percentage of Republican voters. The answer requires determining the adequacy of the sample size, the mean of the difference in sample proportions, the deviation of the difference and probability.