Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 16 minutes. Consider Let X = the average of the 49 races. Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) X - N 143 2.29 Part (b) Find the probability that the average of the sample will be between 142 and 146 minutes in these 49 marathons. (Round your answer to four decimal places.) .6247 XSalaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district. Part (a) In words, define the random variable X. O the number of teachers in an elementary school in the district O the number of teachers in the district the salary of an elementary school teacher in the district O the number of elementary schools in the district Correct! The variable of interest is the salary of one teacher in the district. Part (b) Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.) X - N V 41000 6500 Part (c) In words, define the random variable EX. O the sum of all districts with ten elementary schools the sum of salaries of ten elementary school administrators in the district O the sum of all teachers in ten elementary schools in the district the sum of salaries of ten teachers in elementary schools in the district Part (d) Give the distribution of EX. (Round your answers to two decimal places.) EX - NV 410000 65000 Part (e) Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.) .5596 X Part (f) Find the 80" percentile for an individual teacher's salary. (Round your answer to the nearest whole number.) $ 46460 Part (9) Find the 80" percentile for the sum of ten teachers' salary. (Round your answer to the nearest whole number.) $ 464600X~ N(70, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let EX be the random variable of sums. Part (a) Sketch the distributions of X and X on the same graph. Y X X X O 60 65 70 75 80 60 65 70 75 80 X X X X 70 75 80 O 60 65 70 75 80 60 65 Part (b) Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) X - N | 70 1.8 Part (c) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(X