A scientist claims that 4% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5%? Round your answer to four decimal places.

The probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% is 0.1151.

Step-by-step explanation:

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 size is, n = 553 > 30. Thus, the Central limit theorem is applicable in this case.

Compute the mean and standard deviation as follows:

Compute the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% as follows:

Thus, the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% is 0.1151.

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step-by-step explanation:

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