ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse
ID: 2934919 • Letter: A
Question
ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms.
(a) (5 marks) What is the probability that a filled bag will weigh less than 49.5 kilograms?
(b) (5 marks) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms?
(c) (5 marks) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
(d) (10 marks) ABC is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that 2% of all filled bags weigh more than 52 kilograms?
Explanation / Answer
Ans:
Given that
mean=50
standard dev.=1.25
a)
z(49.5)=(49.5-50)/1.25=-0.5/1.25=-0.4
P(z<-0.4)=0.3446
b)
z(48.5)=(48.5-50)/1.25=-1.5/1.25=-1.2
z(51)=(51-50)/1.25=1/1.25=0.8
P(-1.2<=z<=0.8)=P(z<=0.8)-P(z<=-1.2)
=0.7881-0.1151=0.6731
c)
P(Z>=z)=0.15
P(Z<=z)=1-0.15=0.85
z=NORMSINV(0.85)=1.036
x=50+1.036*1.25=51.3
d)
P(Z>=z)=0.02
P(Z<=z)=0.98
z=NORMSINV(0.98)=2.054
2.054=(52-50)/std dev.
std dev=2/2.054=0.974