what is the approximate probability that fewer than 175 chips will be defective?

Question

Question 5 [12 marks] Each computer chip made in a certain plant will, independently, be defective with probability .2. If a sample of 1,000 chips is tested, what is the approximate probability that fewer than 175 chips will be defective? ( you have to use continuity correction)

Answer 1

so this is a binomial distribution (either can be defective or cannot) so knowing this we will use the calculator to solve::

binomialcdf(1000,.2,174)=2.06%

Think about why it is 174 and not 175.

If you have to write out the formula it is:

₁₀₀₀C₁₇₄(.2)¹⁷⁴(.8)⁸²⁶