Question

To introduce her class to binomial distributions, Mrs. Desai gives a $10$-item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class.

Let $X=$the number of Patti's correct guesses.

To get a passing score on the quiz, a student must guess correctly at least $6$times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.

Short answer

The probability is$0.0064$.

Step-by-step solution

Given Information 

Number of questions$=10$

Students are supposed to guess the answers.

$X$is a number of answers that Patti gives correct.

Explanation 

The binomial distribution pdf is:

$P(X=r)={}^{n}C_r\times p^r\times (1-p{)}^r$

Calculation:

Using Ti-83 plus calculator $P(X<6)$can be calculated as:

Now,$P(X\ge 6)$can be calculated as

localid="1649855112536" $$\begin{gathered} P(X\ge 6)=1-P(X<6) \\ =1-0.9936 \\ =0.0064 \end{gathered}$$