Chapter 5.7, Problem 5E

Let $X_1,X_2,\mathrm{...},X_{48}$ be a random sample of size 48 from the distribution with pdf $f\left(x\right)=\frac{1}{x^2},1<x<\infty$.

Approximate the probability that at most ten of these random variables have values greater than 4. HINT: Let the ith trial be a success if $X_i>4,i=1,2,\mathrm{...},48,$ and let Y equal the number of successes.