A national survey of small businesses reports that 70% of all small businesses now have a
web-site. Assume that for a randomly selected group of 30 small businesses, the number with a
web-site has a binomial distribution.
In a random sample of 30 small businesses, what is the expected number with websites?
To find the expected number with websites in a random sample of 30 small businesses, we can use the formula for the expected value of a binomial distribution.
The expected value (E[X]) of a binomial distribution is given by the formula:
E[X] = n * p
In this equation, n represents the number of trials (in this case, the number of small businesses in the sample, which is 30), and p represents the probability of success (in this case, the probability of a small business having a website, which is 0.70).
Plugging in the values into the formula, we get:
E[X] = 30 * 0.70
Calculating this, we find:
E[X] = 21
Therefore, the expected number of small businesses with websites in a random sample of 30 would be 21.