A manufacturing process produces semiconductor chips with a known failure rate of . If a random sample of chips is selected, approximate the probability that at least will be defective. Use the normal approximation to the binomial with a correction for continuity

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 X = number of defective chips.

The probability that a chip is defective is, p = 0.054.

A random sample of n = 300 chips is selected.

A chip is defective or not is independent of the other chips.

The random variable X follows a Binomial distribution with parameters n = 300 and p = 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:

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 z-table for the probability.

Thus, the probability that at least 14 of the chips will be defective is 0.6664.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !