5-2 Binomial Probability Distributions 231 b. Find the probability of exactly 36 brown M&Ms. c. Find the probability of 36 or fewer brown M&Ms. d. Which probability is relevant for determining whether the result of 36 brown M&Ms is significantly low: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 36 brown M&Ms significantly low? e. What do the results suggest about the 13% claim by Mars, Inc.? 38. Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first 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 first lines for Democrats significantly high? b. Find the probability of exactly 40 first lines for Democrats. c. Find the probability of 40 or more first lines for Democrats. d. Which probability is relevant for determining whether 40 first lines for Democrats is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 first lines for Democrats significantly high? e. What do the results suggest about how the clerk met the requirement of using a random method to assign the order of candidates’ names on voting ballots? 39. Perception and Reality In a presidential election, 611 randomly selected voters were surveyed, and 308 of them said that they voted for the winning candidate (based on data from ICR Survey Research Group). The actual percentage of votes for the winning candidate was 43%. Assume that 43% of voters actually did vote for the winning candidate, and assume that 611 voters are randomly selected. 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 308 voters who said that they voted for the winner significantly high? b. Find the probability of exactly 308 voters who actually voted for the winner. c. Find the probability of 308 or more voters who actually voted for the winner. d. Which probability is relevant for determining whether the value of 308 voters is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 308 voters who said that they voted for the winner significantly high? e. What is an important observation about the survey results? 40. Hybrids One of Mendel’s famous experiments with peas resulted in 580 offspring, and 152 of them were yellow peas. Mendel claimed that under the same conditions, 25% of offspring peas would be yellow. Assume that Mendel’s claim of 25% is true, and assume that a sample consists of 580 offspring peas. 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 152 yellow peas either significantly low or significantly high? b. Find the probability of exactly 152 yellow peas. c. Find the probability of 152 or more yellow peas. d. Which probability is relevant for determining whether 152 peas is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 152 yellow peas significantly high? e. What do the results suggest about Mendel’s claim of 25%?
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