5.5 A nit is a measure of brightness (one nit is equal to one candela per square

Question

5.5 A nit is a measure of brightness (one nit is equal to one candela per square meter). The LCD screens from a manufacturer have brightness, X, that follows a normal distribution (a) Find the probability that a randomly selected screen has brightness between 250 (b) Suppose screens with brightness levels in the highest 25% are sold as "premium" with mean 250 nits and standard deviation = 15 nits, i.e. X ~ N(250, 15). and 270 nits. panels. How many nits must a screen produce to be sold as premium?

Explanation / Answer

Mean is 250 and s is 15. z is (z-mean)/s

a) P(250<x<270) =P((250-250)/15 <z< (270-250)/15)=P(0<z<1.33) =P(z<1.33)-P(z<0)

from normal distribution table we get 0.9082-0.5=0.4082

b) for highest 25% we need to look at value at 75% from bottom i.e 0.75 . Normal distribution table shows that z =0.68 looking at the left most column top most row

thus value is mean+z*s = 250+0.68*15=260.2

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