Suppose that a random sample of size n is selected from a population with mean μ = 750 and standard deviation σ. The Exploring Confidence Intervals applet shows the sampling distribution of x̅ and a representative confidence interval, calculated as

a. The applet loads with n = 50, σ = 35, and x̅ = 756. Calculate the half-width of a 95% confidence interval for μ.

b. Calculate the upper and lower confidence limits and compare these limits to the endpoints of the interval shown in the applet.

c. Does the confidence interval work properly? That is, does it enclose the true value of μ = 750?