7.3 Exercise 55 — Statistics

For each problem, wherever possible, provide graphs and use a calculator.

Large bags of a brand of multicolored candies have a claimed net weight of 396.9 g. The standard deviation for the weight of the individual candies is 0.017 g. The following table is from a stats experiment conducted by a statistics class.

Red (g)	Orange (g)	Yellow (g)	Brown (g)	Blue (g)	Green (g)
0.751	0.735	0.883	0.696	0.881	0.925
0.841	0.895	0.769	0.876	0.863	0.914
0.856	0.865	0.859	0.855	0.775	0.881
0.799	0.864	0.784	0.806	0.854	0.865
0.966	0.852	0.824	0.840	0.810	0.865
0.859	0.866	0.858	0.868	0.858	1.015
0.857	0.859	0.848	0.859	0.818	0.876
0.942	0.838	0.851	0.982	0.868	0.809
0.873	0.863			0.803	0.865
0.809	0.888			0.932	0.848
0.890	0.925			0.842	0.940
0.878	0.793			0.832	0.833
0.905	0.977			0.807	0.845
	0.850			0.841	0.852
	0.830			0.932	0.778
	0.856			0.833	0.814
	0.842			0.881	0.791
	0.778			0.818	0.810
	0.786			0.864	0.881
	0.853			0.825
	0.864			0.855
	0.873			0.942
	0.880			0.825
	0.882			0.869
	0.931			0.912
				0.887

The bag contained 465 candies and the listed weights in the table came from randomly selected candies. Count the weights.

Find the mean sample weight and the standard deviation of the sample weights of candies in the table.
Find the sum of the sample weights in the table and the standard deviation of the sum of the weights.
If 465 candies are randomly selected, find the probability that their weights sum to at least 396.9 g.
Is the candy company's labeling accurate?

OpenStax Statistics, 7.3 Using the Central Limit Theorem, exercise 55

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