Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately click fraud, the practice of someone clicking on an ad solely for the purpose of driving up advertising revenue, has become a problem. Forty percent of advertisers claim they have been a victim of click fraud. Suppose a random sample of 380 advertisers will be taken to learn more about how they are affected. What is the probability that the sample proportion will be with 0.04 of the population proportion?

The probability that the sample proportion will be with 0.04 of the population proportion is 0.8904.

Step-by-step explanation:

Let p = proportion of advertisers who claim they have been a victim of click fraud.

The population proportion is, p = 0.40.

A random sample of 380 advertisers is selected.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

The sample selected is too large, i.e. n = 380 > 30.

Then the proportion of advertisers who claim they have been a victim of click fraud can be approximated by the normal distribution.

The mean and standard deviation of this sampling distribution of sample proportion is:

Compute the probability that the sample proportion will be with 0.04 of the population proportion as follows:

Thus, the probability that the sample proportion will be with 0.04 of the population proportion is 0.8904.

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