Answer:
a) 0.13262
b) 0.66575
c) 0.98076
Step-by-step explanation:
The components manufactured follow a binomial distribution.
In a binomial distribution you have a sequence of independent experiments normally "n" experiments and each experiment in the form of yes or no question with a probability of success "p"
Let X be the variable representing the number of defective components.
The probability of X is calculated as follows for a binomial distribution:
n represents the number of possible defective components
k represents the total number of components
p represents the probability that a component is defective
a)
The probability to fill 100 orders with a stock of 100 components:
n = 0 because you cant have any defective component
k = 100 because thats the available stock
p = 0.02 is the probability of a single component to be defective
b)
The probability to fill 100 orders with a stock of 102 components:
In this case n can take more than one value, because you have 102 components and only need 100 to be good, meaning you are allowed to have 0, 1 or 2 defective components, so you calculate the probability when n = 0, n = 1 and n = 2 and then add them together, also it can be said as calculating n ≤ 2
c)
As b, now n can take more values because the stock is 105, calculating for n ≤ 5,