Question

In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 200 diodes. (a) How many diodes would you expect to fail? 2 Correct: Your answer is correct. diodes What is the standard deviation of the number that are expected to fail? (Round your answer to three decimal places.)

Answer 1

Answer:   a) 2  b) 1.407

Step-by-step explanation:

Given : The probability that any particular diode will fail : p=0.01

The number of diodes in a circuit : n= 200

The number of diodes expected to fail will be :-

$\mu= np=(200)(0.01)=2$  

Hence, the number of diodes expected to fail =2

The standard deviation of the number that are expected to fail will be :-

$\sigma=\sqrt{np(1-p)}\\\\\Rightarrow\sigma=\sqrt{200(0.01)(1-0.01)}\\\\=1.40712472795\approx1.407$ [Rounded to three decimal places.]

Hence, the standard deviation of the number that are expected to fail= 1.407