Answer:
(a) 0.1326
(b) 0.2732
(c) 0.0410
Step-by-step explanation:
Let <em>X</em> = number of defective components.
The probability of <em>X</em> is, P (X) = <em>p</em> = 0.02.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>. The probability mass function of a Binomial distribution is:
(a)
Compute the probability that the 100 orders can be filled without reordering components as follows:
<em>n</em> = 100
Thus, the probability that the 100 orders can be filled without reordering components is 0.1326.
(b)
Compute the probability that out of 102 orders 2 orders needs reordering as follows:
<em>n</em> = 102
Thus, the probability that out of 102 orders 2 orders needs reordering is 0.2732.
(c)
Compute the probability that out of 105 orders 2 orders needs reordering as follows:
<em>n</em> = 105
Thus, the probability that out of 105 orders 5 orders needs reordering is 0.0410.