Final answer:
True, if the statement relates to the mean of the sampling distribution being approximately the same as the population mean, which is consistent with the central limit theorem assuming a large enough sample size.
Step-by-step explanation:
A student asked whether it is true or false that a population of VC sales has a normal distribution with a mean (μ) of 141 and a standard deviation (σ) of 62.5, given that they intend to draw a random sample size of n=148. The statement they are asking to validate is not entirely clear as it lacks context, but here are some facts that may help:
True. If the student meant that the sampling distribution of the sample means will have a mean equal to the population mean (141 in this case), then this statement is true. This is confirmed by the central limit theorem which states that, given a sufficiently large sample size (usually n > 30), the sampling distribution of the sample means will be approximately normally distributed, with the same mean as the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (the standard error).
Therefore, the sampling distribution of the sample means for VC sales, with n=148, would approximate a normal distribution with a mean (μ) = 141 and a standard deviation (standard error) = 62.5 / √148.
If the statement relates to the population distribution, we can infer based on the described scenario that the student is likely referring to the central limit theorem's implications on the sampling distribution, not the population distribution itself. The characteristics of the population distribution were already given as normal with specified mean and standard deviation.