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

Question

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 with mean µ = 250 nits and standard deviation = 15 nits, i.e. X N(250, 15).

(a) Find the probability that a randomly selected screen has brightness between 250 and 270 nits.

(b) Suppose screens with brightness levels in the highest 25% are sold as “premium” panels. How many nits must a screen produce to be sold as premium?

Explanation / Answer

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

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

from normal distribution table we can find the probability as 0.9082-0.5=0.4082

b) for the top 25%, we need to look at the probability from the bottom as the value at 1-0.25 or 75%

thus for 0.75, the z value from the normal distribution table is 0.68

therefore answer is mean+z*s =250+0.68*15=260.2

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