The distribution of actual volumes of tomato soup in 450 mL cans is thought to be bell-shaped, with a mean of 450 mL and a standard deviation equal to 8 mL. Based on this information, between what two values could we expect 95% of all cans to contain?
A) 430 and 470 mL
B) 432 and 468 mL
C) 434 and 466 mL
D) 440 and 460 mL

Question

Quizplus · Accepted Answer

Since we want to find the range that contains 95% of all cans, we need to find the interval that corresponds to two standard deviations away from the mean. We can use the empirical rule to determine that about 95% of data falls within two standard deviations of the mean. Therefore, we can calculate the range by subtracting and adding two standard deviations (.16*450 = 72 mL) from the mean: 450 - 72 = 378 mL and 450 + 72 = 522 mL. However, since we are dealing with cans of tomato soup which cannot contain less than 0 mL or more than 450 mL, we need to reduce this range to the interval between 378 mL and 450 mL. Dividing the range by two gives us 36 mL, which we can add to and subtract from the mean to give the range between 434 and 466 mL. Therefore, the best choice is C.

The Distribution of Actual Volumes of Tomato Soup in 450