03.1 Mean of T 0.5 Points A meal package for use at the space station is to be prepared by combining three separate components: protein, fruit/vegetable, and grains. Each of the components is to be randomly selected. Summary values for the caloric content for each of the components are given in the table. ' Mean Stdv Component (calories) (calories) n-II Assume that the distributions of caloric content for each of the components are approximately normally distributed. Since the meal package consists of protein, fruit/vegetable, and grains, the total caloric content of a meal package is the random variable T, where T = P + F + G. Find the mean of T. Show your work appropriately. 03.2 Standard Deviation of T 1 Point A meal package for use at the space station is to be prepared by combining three separate components: protein, fruit/vegetable, and grains. Each of the components is to be randomly selected. Summary values for the caloric content for each of the components are given in the table. . Mean Stdv Component (calories) (calories) nn n Assume that the distributions of caloric content for each of the components are approximately normally distributed. Since the meal package consists of protein, fruit/vegetable, and grains, the total caloric content of a meal package is the random variable T, where T = P + F + G. Find the standard deviation of T. Show your work appropriately. 03.3 Normal, but why? 1.5 Points A meal package for use at the space station is to be prepared by combining three separate components: protein, fruit/vegetable, and grains. Each of the components is to be randomly selected. Summary values for the caloric content for each of the components are given in the table. Mean Stdv Component (calories) (calories) Protein (P) 120 Fmitfvegctable (F) Grain (G) Assume that the distributions of caloric content for each of the components are approximately normally distributed. Since the meal package consists of protein. fruit/vegetable, and grains, the total caloric content of a meal package is the random variable T, where T = P + F + G. Briefly explain why it is appropriate to say that T is approximately normally distributed. Q3.4 Probability Less than 275 Calories 3 Points On your own piece of paper find the approximate probability that a randomly selected meal package will have less than 275 calories? (Draw an appropriate diagram, find a z-score and indicate your calculator commands.)