Distribution of Sample Proportion Question

djwatson

New Member
Hi, apreciate any help anyone can give. I'm currently teaching myself A-level statistics from 'A Concise Course in A-Level Statistics' and I'm stuck on the below topic.

In the following example, I followed it through and understood how the process worked (or so I thought!)  I followed up to this point and then used the calculator rather than the Z-tables as the syllabus has retired these and specifically advises students to use a calculator instead.
Using Normal CD mode, I input the following - Lower: 0.049, Upper: 1, SD: 0.0076, mean: 0.03.
I got the answer of 0.0064 which matches that given in the example. So far so good.

However, in practice, I struggled to apply this although I'm sure I'm following the same process and have been back over it quite a few times, so if anyone can help me out I'd be so grateful. As you can see, my answer is 0.1446, but the answer the book gives is 0.0745, but I'm unclear where I've gone wrong along the way as I can't see that I've done anything differently than in the worked example.

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obh

Well-Known Member
Hi DJ,

You may try to use the binomial distribution.
1% of 300 is 3, but since the distribution is discrete, less than 3 means ≤2, not ≤3

(the other example state 5% or more so it includes the 5%)

djwatson

New Member
Hi DJ,

You may try to use the binomial distribution.
1% of 300 is 3, but since the distribution is discrete, less than 3 means ≤2, not ≤3

(the other example state 5% or more so it includes the 5%)
I did try doing it that way and ended up with the same answer. I also was taught in this book that because of the discrete/continuous you need to make continuity corrections which are + 0.5 on the top parameter and - 0.5 on the bottom parameter, so I thought trying it this way that P(X<3) becomes P(X<3.5)?

obh

Well-Known Member
I did try doing it that way and ended up with the same answer. I also was taught in this book that because of the discrete/continuous you need to make continuity corrections which are + 0.5 on the top parameter and - 0.5 on the bottom parameter, so I thought trying it this way that P(X<3) becomes P(X<3.5)?
You can't get the same result if you replace 3 by 2....