The distribution of piston diameters is normally distributed

The distribution of piston diameters is normally distributed. It is known that 10% of all pistons have diameters exceeding 20 inches and 5% have diameters smaller than 10 inches. What are the mean and SD of the distribution?

Similarly, The distribution of resistance for certain types of resistors (measured in ohms) is normally distributed with mean and standard deviation . What should the value of be if we want to make sure than 90% of the resistors have resistances that are within 4 ohms of the mean ?

Solution

The distribution of piston diameters is normally distributed. It is known that 10% of all pistons have diameters exceeding 20 inches and 5% have diameters smaller than 10 inches. What are the mean and SD of the distribution?

As

x = u + zs

and for the top 10%,

z = 1.281551566

Thus,

20 = u + 1.281551566 s

Also, for the lower 5%,

z = -1.644853627

Thus,

10 = u + (-1.644853627)s

Thus,

u = 15.62073096
s = 3.417161788 [ANSWER]

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