Answer to Question #334761 in Statistics and Probability for Caryna

Question

Note: Assume that the population is infinite in this case and solve.

Problem: The scores of individual students on a national test have a normal distribution with mean 18.6 and standard deviation 5.9.At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, what are the mean and standard deviation of the sample means for 76 students.

Table:

Steps Solution

1.Identify the given formation.

2.Find the mean of they sampling distribution. Use the property that Mx=M

3.find the standard deviation of the sampling distribution.

Answer 1

1. Let $\bar{X}=$ sample mean: $\bar{X}\sim N(\mu, \sigma^2/n).$

2. $\mu_{\bar{X}}=\mu=18.6$

3. $\sigma_{\bar{X}}=\sigma/\sqrt{n}=\dfrac{5.9}{\sqrt{76}}\approx0.6768$