Pilferage at a potato chip factory? The distribution of weights of “jumbo” bags
ID: 3356984 • Letter: P
Question
Pilferage at a potato chip factory? The distribution of weights of “jumbo” bags of potato chips produced at a particular potato chip packing plant is supposed to have µ = 32 ounces and = 1 ounce. The morning-shift supervisor at a potato chip packing plant suspects that the night-shift workers underfill the bags (and eat what they are not packing). The morning-shift supervisor plans to investigate by weighing a random sample of bags of potato chips filled on the night shift. (sample size for part a: 4 sample mean: 31.8 sample size for part c :144)
a) The size (use sample size for part a) and mean of the random sample of bags weighed by the supervisor are shown in the table above. Assuming that the weights of bags are distributed normally with µ = 32 ounces and = 1 ounce (i) calculate the value of z that corresponds to your sample mean in the distribution of means of samples that size (ii) find the probability, P, of obtaining a sample mean that low or lower in the distribution of means of samples that size.
b) Is the value of P that you obtained in part a less than .01? (Answer “yes” or “no”.)
c) Suppose that the morning shift supervisor conducted this investigation with a larger sample (see the table for the sample size for part c) and found precisely the same sample mean. Again assuming that the weights of bags are distributed normally with µ = 32 ounces and = 1 ounce, (i) calculate a the value of z that corresponds to your sample mean in a distribution of means of samples that size, and (ii) find the probability, P, of obtaining a sample mean that low or lower in the distribution of means of samples that size.
d) Is the value of P that you obtained in part c less than .01? (Answer “yes” or “no”.)
e) If your answers in b and d are different (and they should be), explain very briefly why they are different, given that the sample mean is identical in the two situations.
Explanation / Answer
a) std error of error =std deviation/(n)1/2 =1/(4)1/2 =0.5
(i) z value =(X-mean)/std error =(31.8-32)/0.5 =-0.4
(ii) probability, P, of obtaining a sample mean that low or lower in the distribution of means of samples that size
=P(Z<-0.4) =0.3446
b) No
c) std error of error =std deviation/(n)1/2 =1/(144)1/2 =0.0833
(i)z value =(X-mean)/std error =(31.8-32)/0.0833 =-2.4
(ii)
P(Z<-2.4)=0.0082
d)
Yes
e)
as we increase the sample size ; variability around mean will reduce as more values concentrate their average on mean,
hence for high sample size margin of error decreases