Question 1207936: Sixty five percent of 12th graders attend school in a particular urban district. If a sample of 450 12th grade children is selected. Find the probability that more than 280 are actually enrolled in the school.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Sixty five percent of 12th graders attend school in a particular urban district.
If a sample of 450 12th grade children is selected.
Find the probability that more than 280 are actually enrolled in the school.
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They want you find the probability that in the sample of 450
12th grade children 280 attend school, if the individual probability is p = 0.65.
The original probability is the Binomial distribution, but since the sample
is very big, it is recommended to use the normal distribution approximation.
For such approximation, the mean of the normal distribution is
m = n*p = 450*0.65 = 292.5;
the standard deviation
SD =  =  = 10.118 (rounded).
So now for this normal distribution we want to find the probability of having X >= 280.
For calculations, you may use your calculator (function normcdf), or Excel spreadsheet (function NORMDIST);
or online calculator https://onlinestatbook.com/2/calculators/normal_dist.html
Do not forget to use the continuity correction factor.
So, for a regular calculator TI-83/84, the function is
z1 z2 m SD <<<---=== formatting pattern
p = normcdf(279.5, 9999, 292.5, 10.118)
Here z1 = 279.5 is the continuity correction factor for 280.
The ANSWER is p = 0.9006 (rounded).
Solved.
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If you are a beginner student in learning probability distributions, I advise you to start learning
this kind of computations using the online calculator, to which I referred above.
It provides a graphical support, so at each step you do understand what you are doing.
In addition, this graphical support prevents you from making mistakes.
When you learn enough this kind of computations, you can switch to your regular calculator,
but even then you may use the online calculator for checking purposes.
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