Question

Suppose that replacement times for washing machines are normally distributed with a mean of 11 years and a standard deviation of 19 years Find the replacement time that separates the top 18 from the botom 82% Round to the neareste Click to view.nage the love of the O A 12 years OB 127 years O C. 113 years OD 9 years

Answer 1

Also, it is > pdf of 2 11 a 1.9 a- 11 = Let, x be a random variable denoting the replacement times foro washing machines. (unit: years) given that: x^ Normal Cu= 11,0 = 1.9) Let, a be the point Chere, the replace - y ment time) that separates the top 18% from the bottom 82% , so it is given that the X~ N(HE 11.0=19 area at the left of the point a=0.82. 82% If we define, L = _X-le (X- 11 tion. Then, ž~ Normal (p=0, 6-1) ie, standard normal distribu- Required value of the point a can be obtained as followa PCX <a) = 0.82 X-11 < -0.82 1.9 19 => P(Z < 9+4) - = 0.82 Ler, 80 bę CDF of a standard normal distribution, then we can corite - a - 11 $ € )-0.82 1.9 a -11 D-0.82) 1:9 11 +£4.9 * $ (0.82) Using z- table, we get (0.82) 0.915) :: Q ~ 11+ (1.9 x 0.915) => a ñ 12.7 Answer: The required replacement time that separates the top 18% from the bottom 82% 3 i8 = 12.9 years Correct choice:B. 12.4 years. a=