Question

The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kilograms per square centimeter and a standar deviation of 100 kilograms per square centimeter

c) what strength is exceeded by 95% of the samples?

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

a) what is the probability that a laser fails before 5000 hours?

Suppose that the timeto failure in hours of fans in a personal computer can be modeled by and exponential distribution with landa=0.0003

b) what proportion of the fans will last at most 7000 hours

Answer 1

Solution:

c)

Given that

mean of 6000 kilograms

standard deviation of 100 kilograms

strength is exceeded by 95% of the samples

0.95 = P( Z > x - 6000 / 100) = 1 - (x - 6000 / 100)

x - 6000 / 100 = 0.05

using tables we get
x - 6000 / 100 = -1.645
x = 5835.5 = 5835

a) Given that

mean of 7000 hours

standard deviation of 600 hours

probability that a laser fails before 5000 hours

P( X < 5000) = P( Z < 5000 - 7000 / 600)

=P( Z< -3.33)

Using standard normal table

1−P ( Z<3.33 )=1−0.9996=0.00039

b)

Let X be exponnetial distributed normal variable

λ = 0.0003

proportion of the fans will last at most 7000 hours

P(X < 7000) = F(7000) = 1-2-3/10000X7000 0.8775

Answer 2

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