answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N( b. What is the distribution of ¤? ¤ ~ N( c. What is the distribution of ) x? Σε-Ν( d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.5781 and 23.9781 minutes. e. For the 40 runners, find the probability that their average time is between 23.5781 and 23.9781 minutes. f. Find the probability that the randomly selected 40 person team will have a total time more than 964. g. For part e) and f), is the assumption of normal necessary? h. The top 10% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship No Yes round? minutes Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ U( b. Suppose that 36 people are surveyed. What is the distribution of x for this sample? I c. What is the probability that the average birth month of the 36 people will be less than 6.8? N(

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