1. Create a probability distribution where x represents the number of girls in 3 births. Assume the probability of having a boy and a girl is equal. Hint: Write out the sample space, first. 2. Determine whether the following is a probability distribution or not. If it is, find the mean. If it is not, justify why it isn't. The random variable, x, represents the number of people in groups of 6 who say their partner and/or family contribute most to their happiness in a Coca-Cola survey. P(x) 0 0+ 1 .003 2 0.025 3 0.111 4 0.279 5 0.373 6 0.208 3. Use the following probability distribution to answer the questions below. The probability distribution describes results of an inspection of camping chairs. The random variable, x, represents the number of chairs that had defects among the groups of five that were inspected. Find the probability that: a. Exactly 3 chairs had defects b. At least 3 chairs had defects C. Less than 3 chairs had defects X P(x) 0 0.250 1 0.298 2 0.229 3 0.168 4 0.034 5 0.021 4. Based on results from n AARP survey, assume 74% of adults have a credit card. If 20 adults are randomly selected, use StatCrunch to find the following probabilities. State your values for n, p, and x. a. Exactly 15 adults have a credit card b. At least 15 adults have a credit card c. Less than 15 adults have a credit card d. All 20 adults have a credit card e. None of them have a credit card 5. Based on a USA Today poll, we can assume 53% of adults believe that passwords should be replaced with biometric security, such as fingerprints. We want to recreate this survey with a sample size of 200. a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high for our survey. b. Find the probability of exactly 115 participants in our survey believing passwords should be replaced with biometric security. c. Find the probability of 115 or more participants in our survey believing passwords should be replaced with biometric security. d. Is the probability for part (b) or part (c) relevant for determining if 115 participants is significantly high? e. Based on the relevant probability, is the result of 115 participants believing passwords should be replaced with biometric security significantly high?