Question

A recent study indicated that 60% of all businesses have a web page. Assuming a binomial probability distribution, what is the probability that exactly four businesses will have a web page in a random sample of six businesses?

A. 0.138
B. 0.276
C. 0.311
D. 0.324

Answer 1

The probability that exactly four businesses will have a web page in a random sample of six businesses is 0.138.

Step-by-step explanation:

To solve this problem, we can use the binomial probability formula:

P(X=k) = (nCk) * p^k * (1-p)^(n-k)

Where:

• P(X=k) is the probability of getting exactly k successes
• n is the total number of trials
• p is the probability of success on each trial
• (nCk) is the number of ways to choose k successes out of n trials

In this case, there are 6 trials (sampling 6 businesses) and the probability of success (a business having a web page) is 0.6. Plugging these values into the formula:

P(X=4) = (6C4) * 0.6^4 * (1-0.6)^(6-4)

Calculating this:

P(X=4) = 15 * 0.6^4 * 0.4^2 = 0.138

Therefore, the probability that exactly four businesses will have a web page in a random sample of six businesses is 0.138.