Question

On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 554 pounds and a standard deviation of 63 pounds. The cow transport truck holds 16 cows and can hold a maximum weight of 9488. If 16 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 9488? (This is the same as asking what is the probability that their mean weight is over 593.) (Give answer correct to at least 4 decimal places.)

Answer 1

So, x1,x2,., XiN(55h, 632) [sa(x)=63] Let, X, X, X is be the reighs of the Aniver Cour from a very large herd. 2 So, X, + - +X16= TNN (1sxssh, 16X632) -N (4,02), 4 - 16xsss on 16x632 Ta Total weight of there 16 corr. So, P[T) 9488) 9488 - M 2 - 1 - 4 AN (01) [22 247619 0.0066