Question

Extra Credit Question

If you had a multiple choice test with 53 questions and 3 answer options (assuming that students were responding no better or greater than at chance).

Provide:

1). The expected mean of correct answers.

2). The expected standard deviation associated with that mean.

3). The probability of a student answering 27 or more questions correctly.

Answer 1

here this is binomial with parameter n=53 and p=1/3

1)

expected mean =np=53*1/3 =17.67

2)

expected standard deviation =√np(1-p) =√53*(1/3)*(1-1/3) =3.43

3)

from exact binomial distribution:

P(X>=27)=1-P(X<=26)=

1-∑x=026 (nCx)px(q)(n-x) =

0.0060

from Normal approximation:

probability =P(X>26.5)=P(Z>(26.5-17.67)/3.43)=P(Z>2.57)=1-P(Z<2.57)=1-0.9949=0.0051