Question

Let’s assume that we know the population of SAT math scores for Maine students is normally distributed with a µ = 444 and σ = 115. You randomly select a sample of four students (n = 4) from this population.

(a) Calculate the standard error of the mean, X  .

(b) What is the probability of obtaining a sample mean at or above 500? Also, please illustrate this using a graph.  

(c) Make a graph in which you shade in the area the corresponds to your answer for (b)

(d) What is the probability of obtaining a sample mean as extreme as or more extreme than 400? Also, please illustrate this using a graph.

(e) Make a graph in which you shade in the area the corresponds to your answer for (d)

(f) What is the probability of obtaining a sample mean at or below 355?

(g) Make a graph in which you shade in the area the corresponds to your answer for (f)

(h) What mean scores correspond to the most extreme 5% of sample means?

(i) Make a graph in which you shade in the area the corresponds to your answer for (h)

Answer 1

Question is answered below.