Salaries 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 f 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 O 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 1x Part (e) Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.) .5596 Part (f) Find the 80th 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.) $ 464600 X