Q3.3 Normal, but why? 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. Component Protein (P) Fruit/vegetable (F) Grain (G) Mean (calories) 120 55 84 Stdv (calories) 6.4 1.0 3.6 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.

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Q3.3 Normal, but why?
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.
Component
Protein (P)
Fruit/vegetable (F)
Grain (G)
Mean
(calories)
120
55
84
Stdv
(calories)
6.4
Save Answer
1.0
3.6
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
On your own piece of paper find the approximate probability that a randomly selected meal
package will have less than 269 calories? (Draw an appropriate diagram, find a z-score and indicate
your calculator commands.)
Take a picture of your work and upload where indicated.
Transcribed Image Text:Q3.3 Normal, but why? 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. Component Protein (P) Fruit/vegetable (F) Grain (G) Mean (calories) 120 55 84 Stdv (calories) 6.4 Save Answer 1.0 3.6 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 On your own piece of paper find the approximate probability that a randomly selected meal package will have less than 269 calories? (Draw an appropriate diagram, find a z-score and indicate your calculator commands.) Take a picture of your work and upload where indicated.
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