16. From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. Find the mean, variance, and standard deviation for the defective transistors.

E(x)=0.15

V(x)=0.3075

S(x)=0.5545

Step-by-step explanation:

The mean of a discrete variable is calculated as:

where are the values that the variable can take and are their respective probabilities.

So, if we call x the number of defective transistors in cartons, we can calculate the mean E(x) as:

Because there are 0 defective transistor with a probability of 0.92, 1 defective transistor with a probability of 0.03, 2 defective transistors with a probability of 0.03 and 3 defective transistors with a probability of 0.01.

At the same way, the variance V(x) is calculated as:

Where

So, the variance V(x) is equal to:

Finally, the standard deviation is calculated as:

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step-by-step explanation: