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Let $X_i$ be 1 if we get the $i$th question correct and 0 if not. Then $X_i\sim$ Bernoulli($1/4$) and $X=X_1+\dots+X_{50}$. Then $\mu=1/4$ and $\sigma^2=1/4(1-1/4)=3/16$. Then $$P(X\geq 15)=1-P(X_1+\dots+X_{50}<15)=1-P(\overline{X}<0.3)=1-P(Z<0.816)=1-0.7929=0.2071$$ where $$Z=\frac{\overline X-\mu}{\sigma/\sqrt n}\sim N(0,1).$$
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Sat, 15 Aug 2020 04:41 GMT