Answer: 0.102 or 10.2%.
Step-by-step explanation:
Given : Number of multiple-choice questions = 20
Number of options in any question=4
Each question is worth 5 points and only one response per question is correct.
Probability of getting a correct answer = [tex]\dfrac{1}{4}=0.25[/tex]
If the student needs at least 40 points to pass the test, that mean he needs at-least [tex]\dfrac{40}{5}=8[/tex] questions correct.
Let x denotes the number of correct questions .
By using binomial distribution , we find
[tex]P(x\geq8)=1-P(x<8)\\\\ =1-P(x\leq7)\\\\=1-0.898\ \ \text{[By using binomial table for n= 20 , p=0.25 and x=7]}\\\\=0.102[/tex]
[Binomial table gives the probability [tex]P(X\leq x)=\sum_{x=0}^c^nC_xp^x(1-p)^{n-x}[/tex] ]
Hence, the probability the student passes is closest to 0.102 or 10.2%.
