19:31 11 28 6- . . . 49% unsw.mobius.cloud b) Give reasons why you think the sample mean weight of 63 goats would approximately follow this distribution. (Please keep your answers brief. Note that there are more questions below this free-answer box) A . AT BIUS X X #It 714 Words: 0 c) Calculate the standard deviation of X. (Enter the numerical part of your answer correct to at least 4 decimal places in the box below. ) d) Using the approximation mentioned in question a), what is the probability if you put 63 goats on a "We-got-Goats", their total weight will exceed the maximum allowed weight for this truck? (Enter the numerical part of your answer correct to at least 3 significant figures in the box below.)19:31 11 28 6- . . . 49% unsw.mobius.cloud Some special trucks with two decks are used to carry goats. The one represented below is a model called "We-got-Goats" and it can carry up to 3.1 tons ( = 3, 100 kilograms). Goat A "We-got-Goats" truck used to carry goats It is known that the weight X of a goat follows a distribution with mean u = 49 kilograms and standard deviation o = 1.1 kilograms. Note that this distribution is not symmetric around its mean since there can be very fat goats. The weight of 63 randomly selected goats is recorded. a) What type of distribution does the sample mean weight of goat X (in kilograms) approximately follows, when calculated from 63 goats? O X approximately follows a normal distribution. O X approximately follows a t distribution. O It is impossible to have any idea of the distribution of X since we do not know the distribution of X. O X approximately follows a x2 distribution. b) Give reasons why you think the sample mean weight of 63 goats would approximately follow this distribution. (Please keen your answers hrief Note that there are more questions helow this free-answer hov)