Answer:
The probability that at least 14 of the chips will be defective is 0.6664.
Step-by-step explanation:
The complete question is:
A manufacturing process produces semiconductor chips with a known failure rate of 5.4%. If a random sample of 300 chips is selected, approximate the probability that at least 14 will be defective. Use the normal approximation to the binomial with a correction for continuity .
Solution:
Let <em>X</em> = number of defective chips.
The probability that a chip is defective is, <em>p</em> = 0.054.
A random sample of <em>n</em> = 300 chips is selected.
A chip is defective or not is independent of the other chips.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 300 and <em>p</em> = 0.054.
But the sample selected is too large.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
So, .
Compute the probability that at least 14 of the 300 chips will be defective as follows:
Use continuity correction:
P (X ≥ 14) = P (X > 14 + 0.50)
= P (X > 14.50)
*Use a <em>z</em>-table for the probability.
Thus, the probability that at least 14 of the chips will be defective is 0.6664.
