A company fills bags with fertilizer for retail sale. The weights of the bags of
ID: 3157946 • Letter: A
Question
A company fills bags with fertilizer for retail sale. The weights of the bags of fertilizer have a normal distribution with a mean weight of 15 lbs. and a standard deviation of 1.70 lbs. What is the probability that a randomly selected bag of fertilizer will weigh between 14 and 16 pounds? (Use z for normal distribution) If 35 bags of fertilizer are randomly selected, find the probability that the average weight of the 35 bags will be between 14 and 16 lbs. (Sampling Distribution - Sample mean problem).
Explanation / Answer
For X=14, z=(x-mu)/sigma
=(14-15)/1.70
=-0.58
For X=16, z=(16-15)/1.70
=0.58
Thus P(14<X<16)
=P(X<16)-P(X<14)
=P(z<0.58)-P(z<-0.58)
=0.7190-0.2810
=0.4380
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