Question

7. [7/9 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 6.5.011.NVA MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose x has a distribution with u = 26 and o = 19. (a) If a random sample of size n = 49 is drawn, find je er og and P(26 sās 28). (Round of to two decimal places and the probability to four decimal places.) My = 26 0x = 2.7143 P(26 28) = (b) If a random sample of size n = 66 is drawn, find jeg, og and P(26 57s 28). (Round og to two decimal places and the probability to four decimal places.) My = 26 ox= 2.3399 P(267s 28) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than part (a) because of the larger sample size. Therefore, the distribution about uz is narrower 8. [2/4 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 6.5.013.NVA MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 73 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 73 tons and standard deviation o = 1.4 ton. (a) What is the probability that one car chosen at random will have less than 72.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 27 cars chosen at random will have a mean load weight of less than 72.5 tons of coal? (Round your answer to four decimal places.)

Answer 1

NI 26 19) vug 26 x x 28) g) PI Pix X26) plx 228) Pizx 28-261- Plz«o) 1917 271 n=66 x 2 7 ~ N126, 19 166 81264 x Q28) - P12x28-26 / -plzco). 19166 0-301 & x~ NI3, 14) PIX Q725) P12372.5-73) = P12<-05 co:sl = 10:3605 X ~ N173 1.4 1 دو ۷ P(R 279.5) 112* -0.5 xV23) liu = 12.03.11 ini