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 from that district. Part (a) In words, define the random variable X. O the number of teachers in the district the salary of an elementary school teacher in the district ○ the number of teachers in an elementary school in the district O the number of elementary schools 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 ΣX. O the sum of all teachers in ten elementary schools in the district 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 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- ? ▼ 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 be a more symmetrical normal curve. The distribution would not change. ○ The distribution would shift to the right. ○ The distribution would become an exponential curve. ○ The distribution would shift to the left. 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 take a wider shape. The distribution would shift to the left. The distribution would not change. O The distribution would shift to the right. The distribution would take a more narrow shape.

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 from that district. Part (a) In words, define the random variable X. O the number of teachers in the district the salary of an elementary school teacher in the district ○ the number of teachers in an elementary school in the district O the number of elementary schools 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 ΣX. O the sum of all teachers in ten elementary schools in the district 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 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- ? ▼ 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 be a more symmetrical normal curve. The distribution would not change. ○ The distribution would shift to the right. ○ The distribution would become an exponential curve. ○ The distribution would shift to the left. 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 take a wider shape. The distribution would shift to the left. The distribution would not change. O The distribution would shift to the right. The distribution would take a more narrow shape.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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