1. Fertilizer is sold in bags. The standard deviation of the content of a bag is 0.43 kg. Weights of fertilizer in bags are normally distributed. 40 bags are piled on a pallet and weighted. a) If the net weight of fertilizer in the 40 bags is 826 kg, (i) what percentage of the bags are expected to each contain less than 20.00 kg? (ii) Find the 10 th percentile (or smallest decile) of weight of fertilizer in a bag. b) How many pallets, carrying 40 bags each, will have to be weighed so that there is at least 96% probability that the mean weight of fertilizer in a bag is known within 0.05 kg?
1. Fertilizer is sold in bags. The standard deviation of the content of a bag is 0.43 kg. Weights of fertilizer in bags are
a) If the net weight of fertilizer in the 40 bags is 826 kg, (i) what percentage of the bags are expected to each contain less than 20.00 kg? (ii) Find the 10 th percentile (or smallest decile) of weight of fertilizer in a bag.
b) How many pallets, carrying 40 bags each, will have to be weighed so that there is at least 96% probability that the mean weight of fertilizer in a bag is known within 0.05 kg?
2. An engineering firm produces machines with an average life of 8 years and standard deviation of 2 years. The firm wishes to introduce a warranty scheme in which it would like to replace all the dysfunctional machines under warranty with new ones. But they do not wish to do so for more than 5% of the machines they produce. If the lifespan of the machine is assumed to follow a normal distribution, how long a guarantee period should be offered?
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