Question

Suppose that 73% of the residents in a particular community speak English as their primary language.a. What is the probability that exactly seven out of eight random residents in this community will speak English as their primary language?b. What is the probability that seven or more out of eight random residents in this community will speak English as their primary language?c. Out of a random sample of 40 residents in this community, what is the expected number of residents who would be expected to speak English as their primary language?

Answer 1

Solution

- The formula we shall apply is the Binomial probability formula below:

$\begin{gathered} P(r)=\sum_{r=1}^nnC_rp^rq^{n-r} \\ where, \\ p=\text{ probability of success} \\ q=\text{ probability of failure}=1-p \end{gathered}$

Question A:

- The probability that 7 out 8 random residents in this community is: