Question

Normal Distribution Worksheet 1. The EPA fuel economy estimates for automobile models tested recently predicted a Normal model with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. a. In what interval would you expect the central 68% of autos to be found? b. About what percent of autos should get less than 31 mpg? C. What percent of cars should get between 31 and 37 mpg? d. What percent of cars should get more than 20 mpg? e. Describe the gas mileage of the worst 20% of all cars?

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Answer 1

solution predicted given that the EPA fuel economy estimates for automobiles models tested recently Normal model with mean 24.8 mpg and mfg. (a ) from empirical rule, observations lies within interval deviation 6.2 of standard 68%. رک - د ) uto) to 68.1. an got less 31 mpg Hence of autos be found within interval (24.8 - 6.2, 24.8+6.2) (18.6, 31) (b) that auto than P[X<31 P(x-4 31 - 24.8 =P[2<a 0.5 + Ploca<1) = 0.8413 since rule from pl-1c2 <1] = 0.6826 2 Plocz<1] = 0.6826 ploczai] = 0.3413 Thus, 84.13%. should get less than 31 mpg. 0.5 + 0.3413 empirical of autas

(c) a should Prob that 37 mpy between 31 get and 31- 24.8 6.2 pl 31 < X <31] < x-4 P/1<2 <1.97 Plocz <1.97 37] - Ploczai 37-24.8 6.2 - 0.4756 -0.3413 0.1343 should between 31 and of cars get Thus, 13.43% 37 mpg. (d) a car Prob mpg 20 that should get more than pl X 720] pl X-4 > 20 - 240 Plz z>-0.77 pl-o. 0.77 <2<o] = 0.5 - Ploc Z < 0.47] - 0.5 0.5 -0.2794 than 20 mpy 22.067. = 0.2206 of cars should get more be the cutoff worst 201. cars P ( x cx] = 0.20 e fet X for all

= 0.20 = 0.20 » P{X-4 X- 24.8 - Plz. z cx = 24 0.5-p| 2 - 24 : 22 co] Plocza (X-24.8)] - (since z' is symmetric = 0.20 -) - 030 about o) from z table Płocz<0.84] = 0.299 - 0.3 =) (x-246) - 0.84 T x-29.8 = – 0.84 X 6.2 x = 24.8 -0.84 X 6-2 = 19.59 worst 20-1. of all all cars The gas mileage of is 19.59