Doggie Nuggets Inc. (DNI0 sells large bags of dog food to warehouse clubs. DNI u

Question

Doggie Nuggets Inc. (DNI0 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 31 kilograms and a standard deviation of 1.19 kilograms. Complete parts a through d. below.

a. What is the probability that a filled bag will weigh less than 30.5 kilograms?

b. What is the probability that a randomly sampled filled bag will weigh between 28.9 and 32 kilograms.

c. What is the minimum weight a bag of dog food could be and remain in the top 5% of all bags filled?

d. DNI is unable to adjust the mean of the filling proccess. However, it is able to adjust the standard deviation of the flling process. What would the standard deviation need to be so that no more than 8% of all filled bags weight more than 35 kilograms?

Explanation / Answer

mean is 31 and sd is 1.19

a) P(x>30.5)= P(z>(30.5-31)/1.19)= P(z>-0.42) or 1-P(z<0.42) , from the normal distribution table we get 1-0.6628 = 0.3372

b) P(28.9<x<32)= P((28.9-31)/1.19<z<(32-31)/1.19)= P(-1.76<z<0.84) =P(z<0.84)-(1-P(z<1.76)). From the normal table we get 0.7995-(1-0.9608) =0.7603

c) for top 5% , we mean bottom 95%, for 0.95 area under the curve to its left , referring to the normal distribution table we get 1.65, thus the minimum weight is 31+1.65*1.19 =32.96

d) P(z>35)=0.08

From normal table we need to find the z value for 1-0.08 or 0.92 which is 1.41

Thus (35-31)/sd =1.41 thus sd is 2.84

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