The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams.We calculated the value of z for a specific box of this brand of cereal,and the z value was negative.This negative z value indicates that:
A)We made a mistake in our calculations,as z must always be a nonnegative number.
B)The fill weight exceeds 910 grams.
C)The fill weight is less than 910 grams.
D)The fill weight is equal to 910 grams.
E)The fill weight may be more or less than 910 grams depending on the value of the standard deviation.

Question

Quizplus · Accepted Answer

A negative value of z indicates that the observed value is below the mean. In this case, the observed fill weight is less than the mean fill weight of 910 grams. Therefore, option C, "The fill weight is less than 910 grams", is the correct choice. Option A is incorrect as z can be negative when the observed value is below the mean. Option B and D are also incorrect as they assume that the observed value is equal to or greater than the mean. Option E is incorrect as the value of z depends only on the observed value and the mean, not on the standard deviation.

The Fill Weight of a Certain Brand of Adult Cereal