Question

A simple random sample of size n=10 is obtained from a population that is normally distributed with a mean of 40 and a standard deviation of 3. is the sampling distribution normally distributed?

1. thuhuong
Yes, the sampling distribution is normally distributed because the population is normally distributed.
A sampling distribution is a chance distribution of a statistic obtained from a larger variety of samples drawn from a specific populace. The sampling distribution of a given population is the distribution of frequencies of a variety of various outcomes that would probable occur for a statistic of a populace.
A sampling distribution is a probability distribution of a statistic this is obtained via drawing a huge variety of samples from a particular populace. Researchers use sampling distributions so that you can simplify the technique of statistical inference.
Solution :
mean = μ40
standard deviation σ σ= 3
n = 10
μx =  40
σ x = σ√n =  3/√10  = 0.9487
μ x =  4σ\x = 0.9487
σx = 0.9487
Yes, the sampling distribution is normally distributed because the population is normally distributed.