Based on a survey, $35 \%$ of likely voters would be willing to vote by internet instead of the in-person traditional method of voting. For each of the following, assume that 15 likely voters are randomly selected. Complete parts (a) through (c) below. a. What is the probability that exactly 12 of those selected would do internet voting? 0.00001 (Round to five decimal places as needed.) b. If 12 af the selected voters would do internet voting, is 12 significantly high? Why or why not? Select the correct choice below and fill in the answer box within your choice. (Round to five decimal places as needed.) A. Yes, because the probability of 12 or more is which is low. B. No, because the probability of 12 or more is which is not low. C. No, because the probability of 12 or more is which is low. D. Yes, because the probability of 12 or more is which is not low. c. Find the probabil that at least one of the selected likely woters would do internet voting. 0.0008 (Round to three decimal places as needed.)
Solution
Step 1 ：The problem is asking for the probability of a certain number of successes (internet voters) in a fixed number of trials (15 voters), given a certain probability of success on each trial (35%). This is a binomial probability problem.
Step 2 ：For part a, we need to calculate the probability of exactly 12 successes in 15 trials. The probability is approximately \(\boxed{0.00042}\).
Step 3 ：For part b, we need to calculate the probability of 12 or more successes in 15 trials and determine if this is significantly high. Yes, 12 is significantly high because the probability of 12 or more is approximately \(\boxed{0.00048}\), which is low.
Step 4 ：For part c, we need to calculate the probability of at least one success in 15 trials. The probability that at least one of the selected likely voters would do internet voting is approximately \(\boxed{0.998}\).
