A pharmaceutical company knows that approximately 5% of its birth-control pills have an ingredient that is below the minimum strength, thus rendering the pill ineffective. What is the probability that fewer than 10 in a sample of 200 pills will be ineffective

The probability that fewer than 10 in a sample of 200 pills will be ineffective is 0.4364∴ P(X<10)=0.4364

Step-by-step explanation:

Given that the total number of sample pills is 200

ie., n=200

To find  the probability that fewer than 10 in a sample of 200 pills will be ineffective:

Let us assume it success if a pill is ineffective.

The probability of success in each trial is

∴ p=0.05

We know that the total probability is p+q=1

The probability of failure is q

q=1-p

q=1-0.05

∴ q=0.95

Let X be the random variable of the number of ineffective pills in a sample of 200 pills.

Hence X has Binomial distribution with parameter n=200 and p=0.05

The formula for Mean in Binomial distribution is

Substitute the values in the above formula we get

∴

The formula for Standard deviation in Binomial distribution is

Substitute the values in the above formula we get

∴

Now we have to find the probability that fewer than 10 in a sample of 200 pills will be ineffective.

That is to find the area to the left of x=9.5

The formula is

Substitute the values in the formula we get

∴

Now P(X<10)=P(Z<-0.16)

=0.4364

∴ P(X<10)=0.4364Therefore the probability that fewer than 10 in a sample of 200 pills will be ineffective is 0.4364

The answer to your question is b’(16,14)

Your answer should be 1/3. i hope i could ! good luck : )