The breakdown voltage of a randomly chosen diode of a certai

The breakdown voltage of a randomly chosen diode of a certain type is known to be normally distributed with mean value 40 V and a standard deviation 1.5 V.

A.) What is the probability that the voltage of a single diode is between 39 and 42?

B.) Calculate the 99th percentile of breakdown voltage.

C.) If four diodes are selected independently of one another, what is the probability that all four will have voltage below 42?

Solution

A.) What is the probability that the voltage of a single diode is between 39 and 42?

P(39<X<42) = P((39-40)/1.5 <(X-mean)/s <(42-40)/1.5)

=P(-0.67<Z<1.33) =0.6568 (from standard normal table)

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B.) Calculate the 99th percentile of breakdown voltage.

P(X<x)=0.99

--> P(Z<(x-40)/1.5) =0.99

--> (x-40)/1.5 = 2.33 (from standard normal table)

So x= 40 +2.33*1.5 =43.495

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C.) If four diodes are selected independently of one another, what is the probability that all four will have voltage below 42?

P(X<42) = P(Z<(42-40)/1.5) = P(Z<1.33) =0.9082 (from standard normal table)

So 0.9082^4 =0.68034