Question

The weight of potato chips in a medium sized bag is stated to be 10 ounces. The amount that

the packaging machine puts in these bags is believed to be normally distributed with a mean of 10.2
ounces and a standard deviation of 0.12 ounces. Is it unusual for a bag to contain 9.8 ounces of
chips? Explain your answer.

Answer 1

Explanation:

a normal distribution with mean m and standard deviation d gives us a few regular pieces of information.

for example, we know that 68.2% of all events are within the interval

m ± d

and 95.4% of all events are in the interval

m ± 2d

and 99.7% of all events are in the interval

m ± 3d

that means only 0.3% of all events are outside the interval

m ± 3d = 10.2 ± 3×0.12 = 10.2 ± 0.36

now, when a bag is filled with 9.8 ounces, it is 0.4 off the mean (10.2).

that means it is outside the 10.2 ± 0.36 interval and inside the 0.3% "exception" range.

you have to see it also that way : 0.3% means 3 out of 1000 bags are in that range.

so, yes, it is considered unusual.

Answer 2

No, it is not unusual for a bag to contain 9.8 ounces of chips. This is because the amount of chips in a bag follows a normal distribution, which means that the probability of any given value occurring is determined by its distance from the mean. In this case, 9.8 ounces is only 0.4 ounces away from the mean, which is relatively close and therefore not considered unusual. To put this into perspective, if we look at the probability of a bag containing 9.8 ounces of chips, it would be approximately 0.24 (calculated using the z-score formula). This means that there is a 24% chance of a bag containing 9.8 ounces of chips, which is not considered unusual or rare.

Hope this helps you :)