The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If the battery used to power the computer has a mean time to fail of 60 minutes with a standard deviation of 20 minutes,what is the probability that it will last for a launch of 30 minutes duration without failing?
A)0.9332
B)0.8664
C)0.5668
D)0.4332
E)0.0668

Question

Quizplus · Accepted Answer

To calculate the probability that the battery will last for a launch of 30 minutes without failing, we need to use the normal distribution.

First, we need to find the z-score of the value 30 minutes:

z = (30 - 60) / 20 = -1.5

Next, we use a standard normal distribution table (or calculator) to find the probability of a z-score less than or equal to -1.5. This gives us a probability of 0.0668.

Now, we can use the product rule to find the probability that all three components (gyroscope, computer, and rocket motor) will not fail during the launch:

P(gyroscope does not fail) = 7/10 
P(computer does not fail) = 0.9332 (from the previous step) 
P(rocket motor does not fail) = 9/10

P(all components do not fail) = (7/10) * 0.9332 * (9/10) = 0.5668

Therefore, the probability that the guidance system will not fail during the launch is 0.5668 or approximately 0.57.

The Chief of the Design Team for a New Missile