Question

For the past 30 years, the Industrial Assessment Center (IAC) at Texas A&M University has conducted energy audits of manufacturing facilities in Texas. To date they have audited 780 factories resulting in over $375 million dollars of energy savings. Assume that savings per factory is normally distributed with an average of $484,000 with a standard deviation of $135,000. Based on this information, answer the following questions. Clearly support your answers with calculations. a) What is the range of savings that 80% of the factories are expected to have? b) Based on the data, the top 10 factories (i.e. the factories that saved the most money) saved at least

Answer 1

Solution data 184000 0 Given mean (M) = 484000 S.D (6) = 135000 a let a & b are the extremes of 80% of then plasa = b) = 0.8 pla- 484000 sz s b-135000) =0.8 - 135ooo from normal tables P(-1.28 522 1.28) = 0.8 from eals ① & 2 a-u8u00o = -1.28 135000 135000 - b-484ooo - 1.28 135000 135000 b = 656800 a=311200 the range of saking that 80% of the factories are expected to have between $311200 and $6568000 b) let c be the value at top 10 factories. Plazc) =0.1 then PlaLC) = 0.9 c-484000) = 0.9 - 1 from tables P(Z < 1.28) = 0.9 @ from 0 & 2 C- u8u00o = 1:28 P/2 = 135000 Dom 0 & 12 135000 10 factories saved - 656800 at least $656800 The top