Final answer:
The statement is true; using the Central Limit Theorem, the standard deviation of the sampling distribution of the means for a sample size of 81 is calculated as 5, which matches the given condition.
Step-by-step explanation:
If x represents a random variable with mean 133 and standard deviation 45, we are asked to determine whether the statement that the standard deviation of the sampling distribution of the means with sample size 81 is 5 is true or false. Using the Central Limit Theorem, for a given population with standard deviation σ and sample size n, the standard deviation of the sampling distribution of the sample means (also known as the standard error of the mean) is given by the formula:
σ of the sampling distribution = σ / √n
Substituting the given values:
σsampling distribution = 45 / √81 = 45 / 9 = 5
Thus, the statement is true. The standard deviation of the sampling distribution of the means with sample size 81 is indeed 5.