Question

A student takes an exam containing 14 multiple choice questions. The probability of choosing a correct answer by knowledgeable guessing 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. Answer(How to Enter) 1 Point Tables E Keypad

Answer 1

Solution

$\mathbf{{\color{Blue} given}:}\;n=\mathbf{14},\;p=\mathbf{0.3},\;q=1-p=\mathbf{0.7}$

$\mathbf{{\color{Blue} find}:\;P(At\;least\;9)\Rightarrow P(X\geq 9)=?}$

P(X > 9) = P(X =9) + P(X = 10) +..... + P(X = 13) + P(X = 14)

Use excel formula "=BINOM.DIST(x, n, p, FALSE)"

x	Excel formula	P(X=x) [rounded to four decimal places]
9	=BINOM.DIST(9, 14, 0.3, FALSE)	0.0066
10	=BINOM.DIST(10, 14, 0.3, FALSE)	0.0014
11	=BINOM.DIST(11, 14, 0.3, FALSE)	0.0002
12	=BINOM.DIST(12, 14, 0.3, FALSE)	0.0000
13	=BINOM.DIST(13, 14, 0.3, FALSE)	0.0000
14	=BINOM.DIST(14, 14, 0.3, FALSE)	0.0000

$\\P(X\geq 9)=0.0066+ 0.0014+ 0.0002+ 0.0000+ 0.0000+ 0.0000$

$\mathbf{\\P(X\geq 9)={\color{Red} 0.0083} }$

${\color{red} \mathbf{0.0083}}$