Distribution of Sample Proportion Question

#1
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!)
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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.
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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.

Thanks in advance :)
 

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obh

Well-Known Member
#2
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%)
 
#3
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
#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)?
You can't get the same result if you replace 3 by 2....