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The mean height of women in a country (ages 20 - 29) is 64.3 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume o = 2.75. . . . The probability that the mean height for the sample is greater than 65 inches is (Round to four decimal places as needed.)In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.1 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. . .. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tall is . (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 70 inches. The probability that the study participant selected at random is between 67 and 70 inches tall is . (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 70 inches. The probability that the study participant selected at random is more than 70 inches tall is . (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. O A. There are no unusual events because all the probabilities are greater than 0.05. O B. The event in part (a) is unusual because its probability is less than 0.05. O C. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05. O D. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.In a sample of 800 U.S. adults, 209 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement. Complete parts (a) through (c). . . . (a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is (Round to three decimal places as needed.) (b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is (Round to three decimal places as needed.) (c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models is (Round to three decimal places as needed.)