Question

Not all visitors to a certain company's website are customers. in fact, the website administrator estimates that about of all visitors to the website are looking for other websites. assuming that this estimate is correct, find the probability that, in a random sample of visitors to the website, exactly actually are looking for the website.

Answer 1

To find the probability that in a random sample of visitors to the website, exactly a certain number are looking for the website, you can use the binomial probability formula. The formula involves the probability of a visitor looking for the website, the total number of visitors in the sample, and the number of visitors looking for the website in the sample. Substituting these values into the formula and calculating will give you the desired probability.

Step-by-step explanation:

To find the probability that in a random sample of visitors to the website, exactly a certain number are looking for the website, we can use the binomial probability formula. The formula is:

P(x) = C(n, x) * p^x * (1-p)^(n-x)

Where:

• P(x) is the probability of x visitors looking for the website
• C(n, x) is the number of ways to choose x visitors from a total of n visitors
• p is the probability of a visitor looking for the website
• n is the total number of visitors in the sample

In this case, let's assume that the website administrator estimates that p = 0.7 (70% of visitors are looking for the website) and we want to find the probability that exactly x = 5 visitors are looking for the website in a random sample of n = 10 visitors.

Now we can substitute these values into the formula to calculate the probability:

P(5) = C(10, 5) * 0.7^5 * (1-0.7)^(10-5)

Calculate C(10, 5) as:

C(10, 5) = 10! / (5! * (10-5)!) = 252

Substitute this value and the other values into the formula:

P(5) = 252 * 0.7^5 * 0.3^5

Calculate the result:

P(5) ≈ 0.196

Answer 2

It's a binomial problem with n = 5, p = 0.12 ; x = 4
P(x=4) = 5C4(0.12)^4(0.88)^1 = 5*(0.00030736)(0.88) = 0.000912384..