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In a large shipment of tomatoes, the weight of each tomato is normally distributed with mean...

In a large shipment of tomatoes, the weight of each tomato is normally distributed with mean μ = 4.2 ounces and standard deviation s=1.0 ounce. Tomatoes from this shipment are sold in packages of three.

a) Assuming the weight of each tomato is independent of the weights of other tomatoes, compute the mean of the weight of a package.

b) Assuming the weight of each tomato is independent of the weights of other tomatoes, the standard deviation of the weight of a package is:

c) Compute the probability that a package weighs between 11 and 13 ounces

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In a large shipment of tomatoes, the weight of each tomato is normally distributed with mean μ = 4.2 ounces and standard deviation s=1.0 ounce. Tomatoes from this shipment are sold in packages of three.

Assume that the weight of each tomato is independent of the weights of other tomatoes.

a) Mean of weight of a package is, 4.2 + 4.2 + 4.2 = 12.6 ounces

b) The standard deviation of the weight of a package is,

c) We want to find, P(11 < X < 13)

Therefore, the probability that a package weighs between 11 and 13 ounces is 0.4122

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