A student takes an exam containing 13 multiple choice questi

A student takes an exam containing 13 multiple choice questions. The probability of choosing a correct answer by knowledgeable gussing is 0.3. At least 9 correct answers are required to pass. if the student makes knowledgeable guesses, what is the probability that he will pass? Round your answer to four decimal places.

Solution

A student takes an exam containing 13 multiple choice questions. The probability of choosing a correct answer by knowledgeable gussing is 0.3. At least 9 correct answers are required to pass. if the student makes knowledgeable guesses, what is the probability that he will pass? Round your answer to four decimal places.

n=13

p=0.3

P( x >=9) = 0.0040

Binomial Probabilities Table

X

P(X)

P(<=X)

P(<X)

P(>X)

P(>=X)

0

0.0097

0.0097

0.0000

0.9903

1.0000

1

0.0540

0.0637

0.0097

0.9363

0.9903

2

0.1388

0.2025

0.0637

0.7975

0.9363

3

0.2181

0.4206

0.2025

0.5794

0.7975

4

0.2337

0.6543

0.4206

0.3457

0.5794

5

0.1803

0.8346

0.6543

0.1654

0.3457

6

0.1030

0.9376

0.8346

0.0624

0.1654

7

0.0442

0.9818

0.9376

0.0182

0.0624

8

0.0142

0.9960

0.9818

0.0040

0.0182

9

0.0034

0.9993

0.9960

0.0007

0.0040

10

0.0006

0.9999

0.9993

0.0001

0.0007

11

0.0001

1.0000

0.9999

0.0000

0.0001

12

0.0000

1.0000

1.0000

0.0000

0.0000

13

0.0000

1.0000

1.0000

0.0000

0.0000

Binomial Probabilities Table
	X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
	0	0.0097	0.0097	0.0000	0.9903	1.0000
	1	0.0540	0.0637	0.0097	0.9363	0.9903
	2	0.1388	0.2025	0.0637	0.7975	0.9363
	3	0.2181	0.4206	0.2025	0.5794	0.7975
	4	0.2337	0.6543	0.4206	0.3457	0.5794
	5	0.1803	0.8346	0.6543	0.1654	0.3457
	6	0.1030	0.9376	0.8346	0.0624	0.1654
	7	0.0442	0.9818	0.9376	0.0182	0.0624
	8	0.0142	0.9960	0.9818	0.0040	0.0182
	9	0.0034	0.9993	0.9960	0.0007	0.0040
	10	0.0006	0.9999	0.9993	0.0001	0.0007
	11	0.0001	1.0000	0.9999	0.0000	0.0001
	12	0.0000	1.0000	1.0000	0.0000	0.0000
	13	0.0000	1.0000	1.0000	0.0000	0.0000