Question 1196804
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<font color=red>Answer: 2.5%</font>


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Explanation:


Given info
mu = 70 and sigma = 10
this represents the mean and standard deviation respectively


The 68-95-99.7% Rule is also known as the Empirical Rule.


That rule lays out three basic properties<ul><li>Approximately 68% of the normal distribution is within 1 standard deviation of the mean. </li><li>Approximately 95% of the normal distribution is within 2 standard deviations of the mean. </li><li>Approximately 99.7% of the normal distribution is within 3 standard deviations of the mean.</li></ul>Compute the z score for x = 50
z = (x - mu)/sigma 
z = (50 - 70)/10 
z = -20/10 
z = -2
We're exactly 2 standard deviations below the mean.


We have roughly 95% of the values between z = -2 and z = 2
I.e. P(-2 < z < 2) = 0.95 approximately


That leaves 100% - 95% = 5% of the area for the tails to split up
Each tail gets (5%)/2 = 2.5%


Therefore, about 2.5% of the normally distributed population will have a z score smaller than -2
P(z < -2) = 0.025 approximately 
P(x < 50) = 0.025 approximately when mu = 70 and sigma = 10
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