SOLUTION: A machine is used to regulate the amount of dye dispensed for mixing shades of paint. Suppose the amount of dye dispensed per paint can is normally distributed with a mean of 6 ml
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Question 1132398: A machine is used to regulate the amount of dye dispensed for mixing shades of paint. Suppose the amount of dye dispensed per paint can is normally distributed with a mean of 6 ml and a standard deviation of 0.4 ml.
a) What proportion of paint cans will have more than 6.5 ml of dye?
b) Find the amount of dye that the bottom 2% of paint cans have less than.
c) Suppose that new quality control procedures are introduced that lower the standard deviation from 0.4 to a new value (the mean is still 6 ml). With this new standard deviation, we are told that 98% of the paint cans contain between 5.5 and 6.5 ml of dye. Calculate the standard deviation.
You can put this solution on YOUR website! z=(x-mean)/sd
z>(6.5-6)/0.4 or z>1.25. This has probability of 0.1056
probability is 0.02 at -2.055
-2.055=(x-6)/0.4
x-6=-.822
x=5.178 ml; anything less is the bottom 2%
now-2.055=(-5.5-6)/sd; -2.055=-.5/sd
sd=-.5/-2.055=0.2433 or 0.24
