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# Probability of a Container Containing a Certain Weight

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The weight of the food packed in certain containers is a normally distributed random variable with a mean weight of 400 pounds and the standard deviation of 4 pounds. Suppose that the container is picked at random. Find the probability that it contains:

a) more than 410 pounds
b) less than 398 pounds
c) between 391 and 398 pounds

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#### Solution Preview

a) more than 410 pounds

M = 400, SD = 4
Since the weight follows a normal distribution, we can find the probability by calculating the z value:
Z = (X-M)/SD = (410-400) / 4 = 2.5
From a z table, we find ...

#### Solution Summary

With brief calculations and step by step format, this solution determines probability for each of the conditions for weight of the container.

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