Answer:
Explanation:
Hello!
Your study variable is:
X: number of failure chips in 2000.
This is a discrete variable with the binomial distribution. To check this you have to prove if the variable follows the binomial criteria.
1. The number of observation of the trial is fixed (In this case n = 2000)
2. Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial (As stated in the text, each failure chips are independent of one another)
3. There are two possible outcomes "success" and "failure". The probability of success in the same from one trial to another (In this case our "success" will be a failure chip and the probability of getting one is p= 0.063
So X≈ Bi (n;ρ)
The expected value for a binomial variable is:
E(X)= n*p= 2000*0.063= 126 failure chips
This means that out of the 2000 chips you'd expect 126 to be failures.
The variance for the binomial variable is:
V(X)= n*p*q
Where q is the probability of "failure" of the experiment, in this example we are counting the defective chips as "success" then all working chips are the "failure" of the experiment. This probability is complementary to "p" and you can also find it as "1-p"
V(X)= n*p*q= 2000*0.063*0.937= 118.062
And the standard deviation is the square root of the variance
δ= √V(X)= 10.865 ≅ 10.87
The probability of producing less than 135 defects is:
P(X<135)= 0.78
I've used statistical software to calculate the probability.
I hope this helps!