Question

The S & P 500 is a collection of 500 stocks of publicly traded companies. Using data obtained from Yahoo!Finance, the monthly rates of return of the S & P 500 from 1950 through 2015 are normally distributed. The mean rate of return is 0.007443 and the standard deviation is 0.04135.  

What is the probability that a randomly selected month has a positive rate of return? That is, what is P(X > 0)?

	a.	0.36
	b.	0.68
	c.	0.50
	d.	0.43
	e.	0.57

What is the probability that the mean monthly return for a one year period is positive? That is, for n = 12 months, what is P(the sample mean (x-bar) > 0)??

	a.	0.73
	b.	0.50
	c.	0.57
	d.	0.43
	e.	0.27

What is the probability that the mean monthly return for a three year period is positive? That is, for n = 36 months, what is P(the sample mean (x-bar) > 0)?

	a.	0.86
	b.	0.16
	c.	0.43
	d.	0.92
	e.	0.57

The Connecticut Mastery Test is administered to 6^th graders throughout the state. The Superintendent of Schools in Wolcott decided to acknowledge those students whose scores fell in the top 15% of test scores for their local school system. These students will receive an Award for High Achievement. If scores for 6^th graders in Wolcott are normally distributed with µ = 270 and σ = 24, what is the minimum score a student would need to earn an award?

	a.	301
	b.	312
	c.	286
	d.	290
	e.	295

Answer 1