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.
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 |
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