Question

Two companies, A and B, package snack-size bags of cashews. Let X represent the weight of the packages from company A, and let Y represent the weight of the packages from company B. The mean of X is 2.4 ounces with a standard deviation of 0.3 ounces, and the mean of Y is 1.8 ounces with a standard deviation of 0.5 ounces. Assuming these are independent random variables, which answer choice correctly calculates and interprets the standard deviation of the sum, S = X + Y? Sigma Subscript s = 0.2; companies A and B can expect the total weight of packages to vary by approximately 0.2 ounces from the mean. Sigma Subscript s = 0.34; companies A and B can expect the total weight of packages to vary by approximately 0.34 ounces from the mean. Sigma Subscript s = 0.58; companies A and B can expect the total weight of packages to vary by approximately 0.58 ounces from the mean. Sigma Subscript s = 0.8; companies A and B can expect the total weight of packages to vary by approximately 0.8 ounces from the mean.

Answer 1

The answer choice that correctly calculates and interprets the standard deviation of the sum, S = X + Y is D. Sigma Subscript s = 0.8; companies A and B can expect the total weight of packages to vary by approximately 0.8 ounces from the mean.

What does the standard deviation means?

A standard deviation means the all measure of how dispersed the data is in relation to the mean. It should be noted that low standard deviation means that the data are clustered around the mean, and the high standard deviation means that the data are more spread out.

In this case, the answer choice that correctly calculates and interprets the standard deviation of the sum, S = X + Y is the sigma Subscript s = 0.8; companies A and B can expect the total weight of packages to vary by approximately 0.8 ounces from the mean.

In conclusion, the correct option is D.

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