The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning line positions on voting ballots. Among 41 different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line.
a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 40 top lines for Democrats significantly high?
b. Find the probability of exactly 40 top lines for Democrats.
c. Find the probability of 40 or more top lines for Democrats.
d. Which probability is relevant for determining whether 40 top lines for Democrats is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 top lines for Democrats significantly high?
e. What do the results suggest about how the clerk met the requirement of assigning the line positions using a random method?