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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.