Answer
a)0.5.
b)0.44.
c)p is between 0.44-0.0764=0.3636 and 0.44+0.0764=0.5164.
d)The ability doesn't seem to be too good.
Work Step by Step
a) One choice is correct out of the two, so the expected proportion is: $p=\frac{1}{2}=0.5.$
b)The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{123}{280}=0.44.$
c)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=2.575\cdot \sqrt{\frac{0.44\cdot (1-0.44)}{280}}=0.0764.$
Hence, the confidence interval: E is between $\hat{p}-E$ and $\hat{p}+E$, hence p is between 0.44-0.0764=0.3636 and 0.44+0.0764=0.5164.
d)The ability doesn't seem to be too good, because the expected proportion us in the confidence interval.
