Question

Yes sin ☺ (A) SUPPOSE A MULTIPLE CHOICE Quiz Bing HAS 10 QUESTIONS. EACH QUESTIOU p - Plright answers) "answeis) HAS 5 POSSIBLE ANSWERS: a, b, c, d ore. ASSUME You ARE GUESSING THE ANSWER TO EACH QUESTION. (0) Write Out A MATHEMATICAL EXPRESSION FOR THE PROBABILITY OF GUESSING 4 OR MORE CORRECT AW SWERS. (i) How MANY CORRECT ANSWERS DO you EXPECT TO OBTAIN? WHAT is THE STANDARD DEVIATION?

Answer 1

Solution:

We are given:

$n=10, p=\frac{1}{5}=0.20$

(i)

Let x be the number of correct answers.

$P(x \geq 4)$

We know that:

$P(x \geq 4)=1-P(x<4)$

(ii) The expected number of correct answers are:

$\boldsymbol{E(x)=np=10 \times 0.2=2}$

The standard deviation is:

$\boldsymbol{Std(x)=\sqrt{np(1-p)}=\sqrt{10 \times 0.2 \times (1-0.2)}=1.2649 }$