S3 inequality confusion

https://postimg.cc/gallery/2znkbxmho/

Hi guys , I’m stuck on part 26 c . I didn’t use an inequality in my answer . I got 57 but I didn’t use inequalities but I think I was supposed to . My question is why do we use an inequality here to get n . I have seen other types of questions before which are pretty much the same but don’t involve an inequality to find n . So when are we supposed to use it ?

Thank you :smile:

Reply 1

Angels1234

https://postimg.cc/image/acfhe6w8r/ in this question part c is a type of question I was talking about which doesn’t use an inequality. What is the difference in the wording of these questions that should be a trigger for when to or not to use inequalities?

Reply 2

RDKGames

Study Forum Helper

Original post by Angels1234

The trigger here is the phrase 'at least'

If X is at least as a big as Y then

X \geq Y

.

Phrases like 'more than' imply strict inequality, ie size X is more than size Y then

X > Y

(edited 5 years ago)

Reply 3

Angels1234

Original post by RDKGames

The trigger here is the phrase 'at least'

If X is at least as a big as Y then

X \geq Y

The thing is in the alternative link I posted above the other question is also at least 0.9 so what makes that question different to this one in terms of using the inequality sign ?

Reply 4

Angels1234

Original post by RDKGames

The trigger here is the phrase 'at least'

If X is at least as a big as Y then

X \geq Y

.

Phrases like 'more than' imply strict inequality, ie size X is more than size Y then

X > Y

in the other link the question was that the probability of the positive difference is less than 0.5 . What is it about it being a less than and not a less than or equal sign that means we dont require and inequality\?

Reply 5

old_engineer

Original post by Angels1234

My take on this is that if the question asks for “the minimum value” you should only be expected to state that value, not a range. However, to be on the safe side, I would suggest writing something like “the minimum value is” <value>.

One thing that can happen is that the working naturally involves an inequality, leading to an answer like n >= 7.3. If n is an integer quantity, you should finish by saying “the minimum value of n is 8”.

Reply 6

Angels1234

Original post by old_engineer

I don’t know when I should be involving an inequality though. Like why can’t we always use an equal sign and then round up the decimal answer we get

Reply 7

RDKGames

Study Forum Helper

Original post by Angels1234

The thing is in the alternative link I posted above the other question is also at least 0.9 so what makes that question different to this one in terms of using the inequality sign ?

It's not that different, you should really use

\geq

as then you you get down to

n \geq ...

or whatever. It says 'at least 95%' hence

\geq 0.95

and this means that

|z| \geq 1.96

and hence

\dfrac{1.25}{\frac{\sigma}{\sqrt{n}}}>\dfrac{|\mu-\bar{X}|}{\frac{\sigma}{\sqrt{n}}} \geq 1.96

which impies that

\dfrac{1.25}{\frac{\sigma}{\sqrt{n}}} > 1.96

hence

n > 56.64...

.

Anyway, you're dealing with a continuous distribution here, whether you choose

>

\geq

really makes no difference.

Reply 8

old_engineer

Original post by Angels1234

I don’t know when I should be involving an inequality though. Like why can’t we always use an equal sign and then round up the decimal answer we get

A couple of thoughts about that. First, it may just be a bit easier for the examiner to see what you’re up to if you work with the inequality (when appropriate). Second, the quantity you’re interested may end up on the other side of the inequality, through rearrangement. There is a risk you may miss this if you work with “=“.