Final answer:
Normal distributions are symmetric about their mean with the area under the curve equal to one, and standard deviation affecting the spread. Without additional data to pinpoint the mean, options with a standard deviation of 4 match the known standard deviation of the population being sampled. Therefore, either 'Mean = 30, Standard deviation = 4' or 'Mean = 28, Standard deviation = 4' could be correct.
Step-by-step explanation:
The question pertains to identifying the mean and standard deviation of a normal distribution, which can be determined by understanding the properties of a normal distribution curve. Normal distributions are symmetric around their mean, and the standard deviation determines the spread of data around this mean. The area under a normal distribution curve totals to one, and the mean, median, and mode of a normally distributed population are all equal.
To estimate the mean (μ) and standard deviation (σ) of a normal distribution when we know the properties of the population from which samples are drawn, we look at the statements provided. Given a normally distributed population with a standard deviation of four and assuming a sample size of 30, the estimate closest to a standard deviation of 4 would be the most probable option. From the choices given, the options with a standard deviation of 4 are those with means of 30 and 28.
Without further information about the actual location of the mean, we cannot definitively conclude which of these two is correct solely based on the standard deviation. Typically, additional information such as a sample mean would help us narrow down the choice of the population mean. In the absence of such additional data, we could guess but would do so without adequate evidence for a definitive conclusion. However, based on the standard deviation information, the options with a standard deviation of 4 would be the most likely, eliminating other choices with different standard deviations.
Therefore, since we need to select an answer, and we have narrowed it down to two choices both having the correct standard deviation of 4, we would either need to guess or obtain more information to choose confidently between: Mean = 30, Standard deviation = 4 and Mean = 28, Standard deviation = 4.