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 z value indicates that the observed fill weight is less than the mean fill weight of 910 grams. As z is calculated using the formula (observed value - mean) / standard deviation, a negative value indicates that the observed value is less than the mean. Therefore, option C is the correct answer. Option A is incorrect as z can be negative if the observed value is less than the mean. Option B is incorrect as it contradicts the negative z value obtained. Option D is also incorrect as it assumes that the z value is zero, which is not the case. Option E is also incorrect as the sign of z does not depend on the standard deviation.

The Fill Weight of a Certain Brand of Adult Cereal