Final answer:
The expected standard deviation of the mean speeds of the random sample of aircrafts, also known as the standard error, is 14.14 mph. This is calculated using the population standard deviation and the square root of the sample size. So the correct answer is option C.
Step-by-step explanation:
Expected Standard Deviation of a Sample
When you have a population with a known mean and standard deviation, and you take a random sample from that population, the standard deviation of the sample mean, also known as the standard error, can be calculated. It is important to note that the question seems to be asking for the standard deviation of the sample mean, not the standard deviation of the sample itself, which would remain the same as the population's standard deviation, assuming the sample is drawn randomly and is representative.
The formula to calculate the standard error (SE) of the sample mean is:
SE = σ / √n
where:
- σ is the standard deviation of the population
- n is the size of the sample
Given that the population standard deviation (σ) is 200 mph, and the sample size (n) is 200, the calculation is as follows:
SE = 200 / √200 = 200 / 14.14 ≈ 14.14 mph
Therefore, the expected standard deviation of the mean speeds of the aircrafts in the random sample is 14.14 mph.