Question

the letter "t" estimated makes up 10% of a language. a random sample of 700 letters is taken from a book. what is the approximate probability that the random sample of 700 letters will contain 8.9% t's

Answer 1

In this problem, we have a Binomial Probability Distribution

so

n=700

x=700*(8.9/100)=62.3=62

$P(x=62)=\frac{700!}{62!(700-62)!}\cdot0.10^{(62)}\cdot0.90^{(700-62)}$

P(x=62)=0.0313

the aprroximate probability is 3.13%