Question

12. Suppose that X1, X2, ..., X 40 denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X have a probability density function given by 132 0<x<1 o elsewhere The ore is to be rejected by the potential buyer if sample of size 40 X, exceeds 2.8. Estimate P ., X. > 2.8) for the

by central limit theorem

Answer 1

- solution; Oliven that i have a polf given by- flo) = f 34² ornal ale have do estimate thy Plexi 32.8) 431 Central limit theorem says that if xi be indepen- dent random variables such that fli) = Mi and vixi)=8 then random variable y 8xi follows approximately normal distribution with mean u= 2 Mi and variance dal 421 (xi). le Yes N6M, ²) and Yolun Noi Hence, first we have to determine f(xi) and e(x) - l'a. flada D' oyda '*° de (28) Mi ) *)= and E(X)= I x flow dx

Elx): 32 x², alo da 31'34 de . 315-) vcx). Elx?) - {f(x)]² 2. and 48- 45 121 Y = 8; n N Mgo) where u 4x and ME 15780 Yox3 Yu / 30, 2) 2=4-30 NCO

Now Plexi > 2.8) =pl&x - 30 , 2.8-30) 7 Pl / . (2> 27.2 where zu No, 1) 1:225 P[2 7-22-204) - Plzs - 22:204) to use standard normal probability get Plzs -22-204) yo We have table, we PSXi >2.8) 1- xi > 2.8) = 1 121