Question 1127869
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Compute the z score with x = 4, mu = 5.7 and sigma = 1.5
*[Tex \LARGE z = \frac{x - \mu}{\sigma}]
*[Tex \LARGE z = \frac{4 - 5.7}{1.5}]
*[Tex \LARGE z = \frac{-1.7}{1.5}]
*[Tex \LARGE z = -1.13] which is approximate to 2 decimal places


Use a table such as <a href = "http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf">this one</a> to find that *[Tex \LARGE P(Z < -1.13) = 0.1292]


note: look on page 1 for the row that starts with -1.1, then look at the column that has 0.03 at the top. This row and column intersect with the value 0.1292 inside


So this means,
*[Tex \LARGE P(Z < -1.13) = 0.1292]
*[Tex \LARGE P(Z > -1.13) = 1-P(Z < -1.13) = 1-0.1292 = 0.8708]
*[Tex \LARGE P(Z > -1.13) = 0.8708]
This is approximate to four decimal places


Therefore,
*[Tex \LARGE P(X > 4) = 0.8708]
which is also approximate


Final Answer: <b><font size=4 color=red>0.8708</font></b>


note: this answer is not entirely perfect due to some rounding errors accumulated. Use a <a href="http://onlinestatbook.com/2/calculators/normal_dist.html">calculator</a> (instead of a table) to get more accurate answer. The reason I'm using a table is that a lot of professors require tables as they are found often in the back of your textbook. 
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