Question

A jopuletion of values hes s normal distribution with μ=87.5 and =5.2. Kou intend to draw a random ample of size n = 1AB, Determine the mean and standert deviation of the sampling distribution of X. Hound solutions to four decimel places, if nectscery Whet is the mean of the sempling distribtion of it 112 What is the standard devietion of the sampines diaribution of at

Answer 1

The mean of the sampling distribution is equal to the population mean (87.5), and the standard deviation is the population standard deviation (5.2) divided by the square root of the sample size (0.52 for n=100), according to the Central Limit Theorem.

Step-by-step explanation:

The student is asking about the mean and standard deviation of the sampling distribution of the sample mean when samples are drawn from a normally distributed population. Given the population mean (μ) is 87.5 and the population standard deviation (σ) is 5.2, we can find these values for the sampling distribution. For the sampling distribution of the mean, the mean (μx) is equal to the population mean (μ), so μx = μ = 87.5. The standard deviation of the sampling distribution (σx) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which in this case is σx = σ / √n = 5.2 / √100 = 5.2 / 10 = 0.52.

This result relies on the Central Limit Theorem, which states that for large sample sizes (n), the sampling distribution will be normal, even if the original population is not normally distributed. This is applicable here as we have a large sample size (n=100).