Question

Doggie Nuggets Inc.​ (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 55 kilograms and a standard deviation of 1.66 kilograms. Complete parts a. through c. below.

a. What is the probability that a filled bag will weigh less than 54.2 ​kilograms?

The probability is (Round to four decimal places as​ needed.)

C.What is the minimum weight a bag of dog food could be and remain in the top 24% of all bags​ filled?

The minimum weight is --- Kilograms

Answer 1

Given that mean =55 and standard deviation=1.66 and also the distribution is normal hence

a) P(X<54,2) is calculated by Z-score calculation, hence Z score at X=54.2

So, p-value for X<54.2 is calculated by finding P-value using the Z statistic table shown below as

P(X<54.2)=P(Z<0.48)

=0.3121

b) Again at the top 24 %, the minimum Z score is calculated using the Z table shown below as Z=0.7, now using Z formula

Hence minimum weight is 56.162 Kilograms.