Question

An Electronic Company is experimenting with the manufacturing of a new type of transistor. Every hour a supervisor takes a random sample of 10 transistors produced on the assembly line. The probability that anyone transistor is defective is considered to be 0.25. The Company is interested in the number of defective parts.

a) Find the probability that from a random sample of 10, there are at most 2 defective transistors .

b) Compute the expected number and standard deviation of 10 defective transistors

Answer 1

Solution:

Let x be a random variable that denotes the number of defective transistors. Then the random variable x follows the binomial distribution with parameters:

a) It is required to find:

We know that:

Now using the binomial probability model, we have:

Therefore, we have:

Therefore, the probability that from a random sample of 10, there are at most 2 defective transistors is 0.5256

b) Compute the expected number and standard deviation of 10 defective transistors

Answer: