Assume that 20 parts are checked each hour and that X

Solution 130E

Step1 of 4:

Let us consider a random variable X it presents the number of parts that require rework. Also we have n = 20 and p = 0.01.

Here our goal is:

a). We need to find the probability that hour 10 is the first sample at which X exceeds 1.

b). We need to find the probability that hour 10 is the first sample at which X exceeds 1.

c). We need to find  the expected number of hours until X Exceeds 1.

Step2 of 4:

a).

Suppose that a random variable X follows binomial distribution with parameters ‘n and p’.

Then, the probability mass function of binomial is distribution is given by:

x = 0,1,2,...,n.

Here, we have n = 20, p = 0.01.

Consider,

Now,