The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Approximate the following probabilities:

(a) More than 25 chips are defective.

(b) Between 20 and 30 chips are defective.

Step 1 of 4:

The percentage of defective chips produced in the manufacturing of semiconductor is 2%

The chips are independent.

A lot contains 1000 chips.

We have to find the following probabilities.

More than 25 chips are defective.Between 20 and 30 chips are defective.Step 2 of 4:

The percentage of defective chips produced in the manufacturing of semiconductor is 2%, p=0.02.

Total number of chips, n=1000.

Let X be the number of defective chips in the manufacturing of semiconductor.

From the given information, it is clear that X~B(1000, 0.02)

So the mean of X,

np= (10000.02).

= 20

The variance of X,

np(1-p)= (10000.020.98).

= 19.6

Since np>5 and n(1-p)>5, normal approximation is valid.

If X is a binomial random variable with parameters n and p,

Z=

Is approximately a standard normal variable.