Answer:
0.1684
Step-by-step explanation:
The whole question is attached.
This is a binomial probability question. The formula is:
[tex]p(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}[/tex]
Where
n is the number in sample (here 36)
p is the probability of "success" (defective means "success", 25% = 0.25)
q is probability of failure (which is 1 - p = 1 - 0.25, q = 0.75)
Now,
we want probability defective LESS THAN 20%, it means:
36* 20% = 7.2
Basically, we want:
P(x < 7.2)
P(x < 7)
Which means P(x < 7) = P(x=0) + P(x=1) + P(x=2) + ..... + P(x=6)
Using cumulative distribution calculator, it will be:
P(x < 7) = 0.1684
