Question

Charlene takes a quiz with 10 multiple-choice questions, each with four answer choices. If she just guesses independently at each question, she has probability 0.25 of guessing right on each. Use simulation to estimate Charlene's expected number of correct answers. (Simulate 20 repetitions using line 122 of this table of random digits. Let 00–24 be a correct guess and 25–99 be an incorrect guess.)

Answer 1

Answer:

Given that,

Charlene takes a quiz with 10 multiple-choice questions, each with four answer choices. If she just guesses independently at each question, she has probability 0.25 of guessing right on each.

Use simulation to estimate Charlene's expected number of correct answers:

Let the X: Number of right answers.

X~Bin(10,0.2)

where n = 10 & p = 0.2

Now let us generate the 20 random observation of from Bin(10,0.2) distribution from excel which are given below:

S.No	X
1	3
2	3
3	2
4	4
5	2
6	3
7	2
8	4
9	3
10	3
11	1
12	2
13	4
14	2
15	3
16	1
17	3
18	1
19	0
20	1
Total	47

Hence the Charlene's expected number of a correct answer is,

= 47/20

= 2.35

Note:

To get the random number, go to the excel Data  Data Analysis( you have to add this add-in from the excel setting if it is not shown in your excel) Random number generation then fill the following details

Number of variable = 1

Number of random number = 20

Distribution = Binomial

Parameters: P-value = 0.2 & Number of trials = 10

Provide the output range to simulate 20 observation from Bin(10,0.2).