Salaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $6,300. We randomly survey ten teachers from that district. Part (a) In words, define the random variable X. the number of teachers in an elementary school in the district the number of elementary schools in the district the number of teachers in the district the salary of an elementary school teacher in the district Part (b) Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.) X- ? Part (c) In words, define the random variable X. O the sum of salaries of ten teachers in elementary schools in the district the sum of salaries of ten elementary school administrators in the district O the sum of all districts with ten elementary schools the sum of all teachers in ten elementary schools in the district Part (d) Give the distribution of X. (Round your answers to two decimal places.) EX-? O Part (e) Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.) Part (f) Find the 90th percentile for an individual teacher's salary. (Round your answer to the nearest whole number.) $ Part (g) Find the 90th percentile for the sum of ten teachers' salary. (Round your answer to the nearest whole number.) $ Part (h) If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part (d)? The distribution would shift to the left. The distribution would be a more symmetrical normal curve. The distribution would not change. The distribution would become an exponential curve. The distribution would shift to the right. Part (i) If each of the 70 teachers received a $3000 raise, graphically, how would that change the distribution in part (b)? The distribution would shift to the left. The distribution would take a wider shape. The distribution would shift to the right. The distribution would not change. The distribution would take a more narrow shape.