Question

9. A computer chip manufacturer knows that 72% of the chips produced are defective.
Suppose 3000 chips are produced every hour, what is the probability that exactly 800
chips are acceptable? Compare the results of using the binomial distributions with
those found using the normal approximation.

Answer 1

The probability that exactly 800 chips are acceptable is less than 0.000001

How to determine the probability?

The given parameters are:

• Sample, n = 3000
• Percentage acceptable, p = 72%
• Acceptable chips, x = 800

The binomial probability is represented as:

$P(x) = ^nC_x * p^x * (1- p)^{n - x}$

So, we have:

$P(300) = ^{3000}C_{800} * (72\%)^{800} * (1- 72\%)^{3000 - 800}$

The data values are large.

So, we use a statistical calculator to evaluate the expression

Using the calculator, we have:

P(300) < 0.000001

Hence, the probability that exactly 800 chips are acceptable is very small i.e. less than 0.000001

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