SOLUTION: A light bulb manufacturer finds that 5% of his bulbs last more than 1000 hours. An improvement in the process meant that the mean lifetime was increased by 100 hours. In a new test
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Question 1089957: A light bulb manufacturer finds that 5% of his bulbs last more than 1000 hours. An improvement in the process meant that the mean lifetime was increased by 100 hours. In a new test, 20% of bulbs now lasted longer than 1000 hours. Find the mean and standard deviation of the original process
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Assuming this is normally distributed,
z=(1000-mean)/sd
z=1.645
1.645*sd=1000-mean
mean=1000-1.645sd
z=0.84
0.84=(1000-(mean+100))/sd
0.84 sd=900-mean
mean=900-0.84 sd
Therefore
900-0.84sd=1000-1.645sd
100=0.805 sd
sd=124.2 hours
mean is 900-104.34=795.7 hours
Check
795.7+(1.645*124.2)=1000.1 or 1000 with rounding.
Mean is 795.7 hours and sd is 124.2 hours
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