Practice variation 2 of 3
Binomial distribution — Fair coin large n
Your question
Let .
(i) Find .
(ii) By finding , show that the standard deviation of is . Hence,
(iii) By using a normal approximation, find the approximate probability that is between and .
This practice question was inspired by Question 12(b) in the 2020 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?