Question

Let X denote the life of a semiconductor laser (in hours) with the following probabilities: P(X ≤ 5000) = 0.05 and P(X > 7000) = 0.45.

a. What is the probability that the life is less than or equal to 7000 hours?
b. What is the probability that the life is greater than 5000 hours?
c. What is P(5000 < X ≤ 7000)?

Answer 1

a) P [ x ≤ 7000] is 0.55

b) P [ x > 5000 ] = 0.95

c) P [ 5000 < x ≤ 7000 ] = 0,5

Explanation:

a) P [ x > 7000 ] = 0.45 straightforward P [ x ≤ 7000] is 0.55

The whole spectrum of probabilities is 1 which in this particular case is divided in two parts having 7000 as a limit, then we subtact 1 - 0.45

b) P [ x ≤ 5000] = 0.05 again we get P [ x > 5000] taking 1-0.05 to get

P [ x > 5000 ] = 0.95

c) P [ 5000 < x ≤ 7000 ]

Under Normal curve distribution the probability of x ≤ 7000 includes values smallers ( to the left of 5000) so we subtract from 0.55 - 0.05 = 0.50

c) P [ 5000 < x ≤ 7000 ] = 0,5