Normal approximation continuity correction question

A random variable X has a binomial distribution with parameters n = 40 and p = 0.3. Use a suitable approximation to calculate P(X=15)

67809E16-08F2-432A-BC9C-9D052D9D4D7A.jpg.jpeg

67809E16-08F2-432A-BC9C-9D052D9D4D7A.jpg.jpeg

Where am I going wrong? I literally cannot see anything wrong with what I’ve done therefore I think I must be doing it wrong altogether. If anyone could help explain it would be appreciated.

Reply 1

Notnek

Original post by _RobbieL_

A random variable X has a binomial distribution with parameters n = 40 and p = 0.3. Use a suitable approximation to calculate P(X=15)

67809E16-08F2-432A-BC9C-9D052D9D4D7A.jpg.jpeg

Where am I going wrong? I literally cannot see anything wrong with what I’ve done therefore I think I must be doing it wrong altogether. If anyone could help explain it would be appreciated.

Your area calculation at the end is wrong. Think about what two areas you are subtracting in your calculation and think about if that would actually give you the shaded region. Please post your thoughts if you're still unusre.

By the way, you should have been able to see that your answer can't be right - with 40 trials it's unlikely that you will get exactly 15 successes (you may have realised this without checking the answer).

Reply 2

_RobbieL_

Original post by Notnek

I realise now that my region calculation was wrong.

Shouldn’t it be P(Z<1.208) - P(Z<0.863)?

I just did this and got an answer of 0.0805, but the actual answer is 0.0808. Where else am I going wrong?

Reply 3

Notnek

Original post by _RobbieL_

How are you working this out? Using tables or your calculator or another method? Your answer is pretty close to the given answer so it might not be worth worrying.

Reply 4

_RobbieL_

Original post by Notnek

How are you working this out? Using tables or your calculator or another method? Your answer is pretty close to the given answer so it might not be worth worrying.

Using the standardised normal distribution tables.

Reply 5

Notnek

Original post by _RobbieL_

Using the standardised normal distribution tables.

Can you please post a link to the tables you are using and tell us the exam board you are doing?

Reply 6

_RobbieL_

Original post by Notnek

Can you please post a link to the tables you are using and tell us the exam board you are doing?

OCR S2, I’m away from my desk now but you should be able to easily look up the OCR formula book online if you want to, or wait until I encourage myself enough to go back to working lol

Reply 7

Notnek

Original post by _RobbieL_

OCR S2, I’m away from my desk now but you should be able to easily look up the OCR formula book online if you want to, or wait until I encourage myself enough to go back to working lol

I get the same answer as you using your tables. Was this a textbook answer or mark scheme answer for an exam question?

I've forgotten how much of a pain it is to use these tables :smile:

Reply 8

_RobbieL_

Original post by Notnek

I get the same answer as you using your tables. Was this a textbook answer or mark scheme answer?

I've forgotten how much of a pain it is to use these tables :smile:

This was a textbook answer so there’s a chance it could be wrong. I’ve got all the questions in this section wrong though so I feel as though I am missing something in my method