Question

The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a standard deviation of 600 hours.

What is the probability that a laser fails after 8500 hours?

What life in hours does 75% of the lasers exceed?

Answer 1

Solution :

Given that ,

mean = = 7000

standard deviation = = 600

a) P(x > 8500) = 1 - p( x< 8500)

=1- p P[(x - ) / < (8500 - 7000) / 600 ]

=1- P(z < 2.50)

Using z table,

= 1 - 0.9938

= 0.0062

b) Using standard normal table,

P(Z > z) = 75%

= 1 - P(Z < z) = 0.75  

= P(Z < z) = 1 - 0.75

= P(Z < z ) = 0.25

= P(Z < -0.67 ) = 0.25  

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 600 + 7000

x = 6598 hours