Question

 

Choices for answers: ONLY ONE ANSWER IS CORRECT
A)
x  P(x)       P(x or fewer)  P(x or greater)
4  0.1167984  0.9510727      0.1657257

B)

x  P(x)       P(x or fewer)  P(x or greater)
4  0.0576782  0.9871216      0.0705566

C)

x  P(x)       P(x or fewer)  P(x or greater)
4  0.0660603  0.9804186      0.0856417

D)

x  P(x)      P(x or fewer)  P(x or greater)
4  0.028672  0.995328       0.033344

E)

x  P(x)      P(x or fewer)  P(x or greater)
4  0.015778  0.9975177      0.0182602

F)

x  P(x)       P(x or fewer)  P(x or greater)
4  0.0057244  0.9994855      0.0062389

PART2: Would five correct answers on the multiple choice test above be significantly high? ONLY ONE ANSWER IS CORRECT

A-No, because the probability is greater than 2.00.

B-No, because the z-score is less than 2.00.

C- No, because the probability is greater than 5%.

D- Yes, because the probability is less than 5%.

E-No, because the z-score is greater than 5%.

F- Yes, because the z-score is greater than 2.00.

G-Yes, because the z-score is greater than 5%.

H-Yes, because the z-score is less than 2.00.

I-Yes, because the probability is less than 2.00.

J-No, because the z-score is less than 5%.

K-No, because the z-score is greater than 2.00.

L-Yes, because the probability is greater than 2.00.

M- No, because the probability is less than 5%.

N-Yes, because the probability is greater than 5%.

O-Yes, because the z-score is less than 5%.

P- No, because the probability is less than 2.00.

Answer 1

n = 7 questions

p = probability of guessing correct answer = 1/8 = 0.125 (there are 8 choices out of which one is correct)

Part 1:

P(Exactly 4 correct answer to the questions) = P(X = 4)

P(At most 4) = P(X < = 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(At least 4) = P(X > = 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

In STATDISK, first select Analysis --------> Probability distributions then select --------> Binomial probabilities

One window will appear , in that plug number of trials as 7 and probability as 0.125 and then click on Evaluate button to get results.

The table with output gives x from 0 to 7 and their corresponding probabilities in the next column.

The probabilities using the STATDISK are,

X	P(X)
0	0.392695904
1	0.392695904
2	0.168298244
3	0.040071011
4	0.00572443
5	0.000490665
6	0.000023365
7	0.000000476837

X = 4

P(X) = 0.0057244

P(X or fewer) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.39265904+0.392695904+0.168298244+0.040071011+0.00572443 = 0.9994855

P(X or greater) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.00572443+0.000490665+0.000023365+0.000000476837 = 0.0062389

Option F is correct.

Part 2:

P(5 correct answers on the multiple-choice) = P(X = 5) = 0.00049066

The probability is less than 5% that is 0.05, which is not significantly high.

Option M is correct.

M- No, because the probability is less than 5%.