Question 1205138
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p = 0.38 = population proportion


phat = sample proportion
phat's job is to estimate p
n = 250 = sample size


Compute the z score when phat = 0.35
z = (phat - p)/( sqrt(p*(1-p)/n) )
z = (0.35 - 0.38)/( sqrt(0.38*(1-0.38)/250) )
z = -0.9772
The result is approximate.


Compute the z score when phat = 0.45
z = (phat - p)/( sqrt(p*(1-p)/n) )
z = (0.45 - 0.38)/( sqrt(0.38*(1-0.38)/250) )
z = 2.2802
This value is approximate as well.


The task of finding P(0.35 < phat < 0.45) is roughly the same as P(-0.9772 < z < 2.2802) when p = 0.38 and n = 250.


Use a stats calculator to find that 
P(-0.9772 < z < 2.2802) = <font color=red>0.8245</font> approximately


I'm not familiar with the wamap stats calculator, so I won't be much help there. Ask your teacher, a classmate, or refer to the wamap help site.


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If you have either a <a href="https://www.statology.org/normal-probabilities-ti-84-calculator/">TI83 or TI84 calculator</a> then type in:
<font color=green>normalCDF(-0.9772, 2.2802, 0, 1)</font> and the approximate result is <font color=red>0.8245</font> when rounding to four decimal places.


Here are some other alternative calculators<ul><li>A <a href="https://davidmlane.com/hyperstat/z_table.html">very user friendly calculator</a> by professor David M Lane. The calculator also displays the shaded diagram which is a nice bonus.</li><li>Use <a href="https://www.wolframalpha.com/">WolframAlpha</a>. Type <font color=green>P(-0.9772 < z < 2.2802)</font> exactly as shown. Make sure the "referring to statistics" option is selected. The WolframAlpha graph is NOT correct so be sure to ignore it (refer to the David M Lane link to see what the graph should look like)</li><li>Use <a href="https://www.geogebra.org/?lang=en">GeoGebra</a>. It can be accessed through either the normal input bar, the CAS mode, or the probability distribution mode. The reference page can be found <a href="https://wiki.geogebra.org/en/Normal_Command">here</a></li><li>Use the <a href="https://support.microsoft.com/en-us/office/normdist-function-126db625-c53e-4591-9a22-c9ff422d6d58">normDist</a> function on a spreadsheet.</li></ul>There are many other alternatives that I haven't listed. You can do an internet search to find your favorite one.
Of all of the choices, the 1st option (the David M Lane one) is probably the best for new students. 
The only drawback is there doesn't appear to be a way to change the precision.


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Answer: <font color=red size=4>0.8245</font> (approximate)
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