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?

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.

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomial probability as a normal probability using the continuity correction.
Binomial Probability Normal Probability
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Find the probability that x = 2 using the binomial tables.
Use the normal approximation to find the probability that x = 2

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Can Nathan use the normal curve area to approximate a binomial probability?

Nathan wants to approximate a binomial probability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomial probability?

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(A) Find the binomial probability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
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Please see the attached file for the fully formatted problems.
1. Explain the difference between a discrete and a continuous random variable. Give two examples of each type of random variable.
2. Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
a