Question

Your math teacher intentionally misinterprets the definition of N99 masks to bring you this challenge." If the diameters of saliva particles are uniformly distributed between 5 and 21 micrometers, how many particles are needed so that the average diameter of the saliva particles is within 3.2 micrometers of the true population mean with at least 99 percent probability?

Answer 1

We need at least 42 particles to estimate the population mean within 3.2 micrometers with 99% confidence.

Explanation:

The problem is not related to the definition of N99 masks, but it involves statistical inference.

To solve this problem, we need to use the central limit theorem, which states that the sample mean of a large sample will be approximately normally distributed, regardless of the underlying distribution of the population.

We can use the formula for the margin of error to find the sample size needed to estimate the population mean within a certain margin of error with a certain level of confidence.

Assuming a normal distribution with a standard deviation of (21-5)/2 = 8 micrometers, we can use the following formula:

Margin of error = z * (standard deviation / sqrt(sample size))

where z is the z-score corresponding to the desired level of confidence. For a 99% confidence level, the z-score is 2.576.

We want the margin of error to be 3.2 micrometers, so we can solve for the sample size:

3.2 = 2.576 * (8 / sqrt(sample size))

sqrt(sample size) = 2.576 * 8 / 3.2

sqrt(sample size) = 6.44

sample size = 6.44^2 = 41.5

Therefore, we need at least 42 particles to estimate the population mean within 3.2 micrometers with 99% confidence.