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QUESTION:

Solve the following items on a clean sheet of paper.

1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?

ANSWER #1

1) 801? Let X be a reandom variable denoting the weight of a goat .. X NN ( 60, 10 ) det X,, X, ... X, be the weights of to randomly selected goats. We are to find ? ( X , + X , + ... X , > 650 ) X, +x, f... Xlo. 650 10 10 = P ( x > 65.@) (x) 0) ? We know, ( 8 ) BAND In then. L J X; = X ~Ne, 5 mm) 1 = 1 (5 ) CWD In our case 80.07 N. N / 60, 10 ) : 1= 60, 17: 10 #, n = 10) - ) X NN ( GO , (TO ) " ) P ( X > 65 ) X - 60 65- 60 VIO 80.0 52 .0 = P ( Z > 1 . 58 ) 80.0 RUN= 0.5- 0.4429 = 0. 05 711. ) The provided information are, M = GO, 0= 10 n = 10 P (Ex > 650) = ? EX VN ( NX = n.M, ox = n2 ) EX V N ( M2 = 600, Ox= 100) P ( 2 x 7650 ) = P Ex- MX 650- MX ox F P / Z Z 650 - 600 100 - P ( 2 7 0 . 5 ) = 0 - 308 5 1 7 From statistical table 76 - 3085