Question

Question 12 of 20 (1 point) View problem in a pop-up The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probabilities. Use a graphing calculator and round the answer to four decimal places. Source: New York Times Almanac. Part 1 A randomly selected teacher earns between $34,000 and $43,000 a year. P(34,000 < X < 43,000) = 0.1937 Correct answer: 0.1938 Part 2 out of 2 A randomly selected teacher earns more than $40,000 a year. P(X > 40,000) = NEXT CHECK

Answer 1

Given, mean , 47,750. Standard deviatino = 5680- Part cans between randomly selected teacher 34,400 and 41,000 a year. Alow pſ24,004 < X < 43,000? ? The corresponding Z values need to be computed. [*, - 14,400 , xy = 43,0007 . . 5 ^ 34,000 - 47.710 - 11730 56 80 5680 !: , - 2.420 Now, to X₂ - 4 43000 47750 -170 5600 5680 "My , -0.8162 Therefore, De get 0 < x < 41000 14000 - 4970 $680 47000 -67710 5680 s pl -2.420 < x < -0.8162)

By Normal distribution, pf 14900 < x < 49000] - 019978 = 0.1938 - part . ? earns more A randomly selected than 40,000 a teacher year distributin function. a pl x y 40000) = ? using normal cofile mermal Cummilative Setting lower = 40000 Allyming upper - 99999 mean (ul> 41750 Arandard deviation (0) = 5680 A p( x17 You on) , 40000 - 49710 1680 -7950 5650 -1.364 By using 't table we get the value 's play 40000) = 0.8624 (ov) 0.869 (assumed value]