WHAT IS THE CORRECT ANSWER?

QUESTION :

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 71The provided information are, M = GO, 0 = 10 n = 10 P ( Ex > 650 ) = ? EX VN ( UX = NM, ox = n? ) EX V N ( My = 400, Ox = 100 ) P ( 2 x 7650 ) = P/ Ex- MX> 650- MX 3 x ox = P / 2 7 650- 600 = P ( 2 7 0 . 5 ) = 0-3085 1 7 From statistical table 76- 3085Solution N= 10 Mean U = 60 - maximum weight = 60X 10 = 600 Standard deviation 5 = 10 As the sample mean is normally distributed with mean u= 60 ; standard deviation 0 = 5 _ 10 = 3.16 The probability that weight of 10 goats will exceed maximum weight is P ( X > 650) = P / Z > 650 - 1x ) = P/ 2>650 - L = ) P/ 2> 650- 600 ) = P ( 2 75 0) = P/ Z> 15.872) 10 3.16 = 0 Answer The random variable ' z ' has standard normal distribution ( mean u,= 0 & standard deviation oz = 1 )