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probability of normal distribution and binomial distribution

3. A production line manufactures 1000 ohms resistors that must satisfy a 10% tolerance.

a. If a resistance is adequately described by a Gaussian random variable for which mean = 1000; and standard deviation = 40;, what fraction of the resistance expected to be rejected?

b. If a machine is not properly adjusted, the product resistances changes, the case where mean= 1050; (5% shift). What fraction is now rejected?

4. At a certain military installation six similar radars are placed in operation. It is known that radar's probability of failing to operate before 500 hours of "on" time have accumulated is 0.06. What are the probabilities that, before 500 hours have elapsed, (a) all will operate, (b) all will fail, and (c) only one will fail?


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It seems the equations could be displayed. Please see the attached file.
Answer to 3: Since the resistance follows the normal function, the probability function is

To calculate the rejection rate of 10% from the mean, we could calculate the acceptation rate first, i.e. the rate the ...

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The solution is comprised of detailed explanations of calculation of probabilities under nomral distribution and binomial distribution.