# Probability: Normal and Binomial Distributions

1. A component in a subsystem has a reliability factor of .9999 during a Shuttle mission. There is redundancy so as long as fewer than 2 of the components fail, the subsystem will operate. What is the probability that there will be 2 or more failures?

2. A video tube has a mean life of 2000 hours with a standard deviation of 200 hours. The life is normally distributed.

a. What part of these video tubes do we expect to have a life greater than 1500 hours?

b. What part of these video tubes do we expect to have a life greater than 2300 hours?

c. What are the number of hours that one of these video tubes can be expected to function with a 95% probability that it will achieve that number of hours without a failure?

If an aircraft cargo door is closed but improperly locked, it is expected that the probability is .003 that it will open in flight. What is the probability of any cargo door opening in flight in a year if 30 doors are improperly locked in a year?

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#### Solution Preview

1. P(2 or more failure)= 1 - P(0 failures)-P(1 failures)

=1-0.9999-0.0001*0.9999

= 0.00000001

2. mean = 2000 SD=200

a) P(X>1500) = ...

#### Solution Summary

This solution provides calculations for various probability questions.