week 3

#1-5

	A teacher gives you a surprise quiz with 10 multiple choice questions, each with 4 possible answers.
	You answer all the questions by randomly guessing.
	Let X = # of correct answers in 10 questions.
1	Determine whether this experiment is binomial or hypergeometric and explain your reasoning? (4 points)
2	Construct the probability distribution table for this experiment. (20 points)
											1	FIXED NUMBER OF TRIALS, n=10
											2	Each trials has two possible outcomes: right or wrong
3	Find the arithmetic mean. (4 points)										3	Assume the trials are independent
											4	Probabilities are constant, p=1/4
4	Find the variance and standard deviation. (8 points)
5	Find the probability of guessing at least 7 correct. (4 points)
	X	P(X)
	0	0.0563135147
	1	0.1877117157
	2	0.2815675735
	3	0.2502822876
	4	0.1459980011
	5	0.0583992004
	6	0.0162220001
	7	0.0030899048
	8	0.0003862381
	9	0.0000286102
	10	0.0000009537
		1
		MEAN	2.5
		VAR	1.9
		SD	1.4
		P(X>=)	0.0035057068	<.05	AT LEAST7

HISTOGRAM

P(X) 0 1 2 3 4 5 6 7 8 9 10 5.6313514709472684E-2 0.18771171569824219 0.28156757354736339 0.25028228759765631 0.14599800109863281 5.8399200439453146E-2 1.6222000122070326E-2 3.0899047851562543E-3 3.862380981445312E-4 2.861022949218752E-5 9.5367431640625E-7

X

P(X)

#6-10

	A shipment of 30 items contains 6 that are defective.
	You are to randomly select 5 different items and test them.
	Let x = the number of defective items among five.
6	Determine whether this experiment is binomial or hypergeometric and explain your reasoning? (4 points)
7	Construct the probability distribution table for the experiment. (20 points)
8	Find the arithmetic mean. (4 points)
9	Find the variance and standard deviation. (8 points)
10	If you accept the shipment only if all the selected items are good,
	what is the probability of rejecting the shipment?
	what is the probability of accepting the shipment? (4 points)
X	P(X)	(X-mean)^2
0	0.2982611258	1
1	0.4473916888	0
2	0.2130436613	1
3	0.0387352111	4
4	0.0025262094	9
5	0.0000421035	16
MEAN	SUM(X*P(X))		1
VAR	SUM((X-mean)^2*P(X))		0.7
SD	sqrt(var)		0.8

#11-15

	It is estimated that 15% of the US population has pet allergies.								12
	Suppose that 80 people are randomly selected.
11	Find the mean and standard deviation for the number of people with pet allergies in groups of 80,										MEAN	12
	assuming the 15% rate is correct. (4 points)										SD
12	Find the probability that exactly 12 people in a group of 80 people have pet allergies. (4 points)
13	Find the probability that 10 or fewer people in a group of 80 have pet allergies. (4 points)
14	Find the probability that at least 11 people in a group of 80 have pet allergies. (4 points)
15	Find the probability that 10 to 20 people in a group of 80 have pet allergies. (4 points)