Answer:
a)






b) 0.154% probability that there are at least 4 defective welders in the sample
Step-by-step explanation:
The welders are chosen without replacement, so the hypergeometric distribution is used.
The probability of x sucesses is given by the following formula:

In which
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:
100 welders, so 
Sample of 15, so 
In total, 5 defective, so 
(a) Determine the PMF of the number of defective welders in your sample?
There are 5 defective, so this is P(X = 0) to P(X = 5). Then







(b) Determine the probability that there are at least 4 defective welders in the sample?

0.154% probability that there are at least 4 defective welders in the sample