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Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with = 77.2 ft and 60 ft. You intend to measure a random sample of n 54 trees. What is the mean of the distribution of sample means? ft What is the standard deviation of the distribution of sample means (i.e., error in estimating the mean)? (Report answer accurate to 2 decimal places.) ft the standard The average number of miles (in thousands) that a car's tire will function before needing replacement is 74 and the standard deviation is 14. Suppose that 44 randomly selected tires are tested. Round z-scores to 2 decimal places for use in calculations. Round all other answers to 4 where possible. Assume that the miles that a car's tire will function before needing replacement is normally distributed. a. What is the distribution of X? X - N b. What is the distribution of i? - N c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 75.7 and 78.9. d. For the 44 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 75.7 and 78.9. e. For part d), is the assumption that the distribution is normal necessary? O NOO Yes SAT scores in one state is normally distributed with a mean of 1598 and a standard deviation of 112. Suppose we randomly pick 56 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1597. > 1597) = b) Find the probability that the average of the scores for the sample of 56 scores is greater than 1597. p(X > 1597) Round each answer to at least 4 decimal places. Suppose scores on the SAT exam are normally distributed with mean 1100 and standard deviation 2 Answer the following. (a) Aaron scored 1044 on the SAT. What proportion of students performed worse than Aaron? Round to 2 decimal places. 500 700 900 tnoo 1300 1500 170t Aaron 's score (b) Betty scored 1177 on the SAT. What proportion of students performed better than Betty? Round to 2 decimal places. 500 700 900 noot 1300 1500 170 Berry's score (c) What proportion of students got a score between Aarons and Bettys scores? Round to 2 decimal places. What score 500 700 (e) What score ts the 92nd percentile of exam scores? Round to the nearest whole number. 1100 1300t 1500 170, 92nd percentile ts the 13th percentile of exam scores? Round to the nearest whole number. 500 700 900 1100 1300 1500 500 700 13th percentile noo 1300 1500 170