Business statistics

1. Blood Donors. Every 2 seconds someone in the U.S. needs blood. People with O-negative blood are called universal donors because their blood can be given to patients of any blood type. Unfortunately, only 6% of people are O-negative. Let X = the number of people with O-negative blood among the next 20 donors who arrive at a blood donation center. X is a Binomial RV (why?). Set up a new worksheet as follows.

	A	B	C	D
1	n =		Number of Trials
2	=		Probability of Success
3
4		x	Binomial probability P(X = x)	Cumulative Binomial probability P(X x)
5		0	=BINOMDIST(B5,$B$1,$B$2,FALSE)	=BINOMDIST(B5,$B$1,$B$2,TRUE)
6		1	copy & paste formula down	copy & paste formula down
: :		: :	: :	: :
25		20	:	:

Make a column chart of the probabilities in cells C5:C25. Make it readable. Label axes appropriately.

1a. Is X’s probability distribution symmetric, skewed left or skewed right? 1b. What is P(3 X 5)?

1c. What is P(X 3)?

1d. What is P(X > 4)?

1e. What is X’s mean (or expected value)?

1f. What is X’s standard deviation?

2. Political Polling. The FiveThirtyEight web site combines results from many polls. As of 3/18/19, this site reported that 42% of Americans approve of the job Trump is doing as president. Suppose that this week a random sample of 200 Americans is contacted. X, the number in the sample who approve of Trump, is a Binomial random variable. Note that X/ n, the sample percentage who approve of Trump, is just a re-scaled version of X, i.e., it takes on values from 0% to 100% instead of 0 to 200, but has the same probabilities as X.

Set up a new worksheet as follows.

	A	B	C	D	E
1	n =			Number of Trials
2	 =			Probability of Success
3
4		x	x/n	Binomial probability P(X = x)	Cumulative Binomial probability P(X x)
5		60	.300	=BINOMDIST(B5,$B$1,$B$2,FALSE)	=BINOMDIST(B5,$B$1,$B$2,TRUE)
6		61	.305	copy & paste formula down	copy & paste formula down
: :		: :	: :	: :	: :
55		110	.550	:	:

Make a column chart of the probabilities in D5:D55. The x-axis should run from 60 to 110.*

2a. P(X/ n < 50%) = P(X < 100) =

2b. P(X/ n < 40%) =

2c. P(X/ n > 45%) =

2d. P(35% X/ n 49%) =

2e. What other distribution looks like X?