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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly...

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 412 gram setting. It is believed that the machine is underfilling the bags. A 99 bag sample had a mean of 405 grams with a standard deviation of 12. Assume the population is normally distributed. A level of significance of 0.01 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

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