Question 1197769
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mu = 2.62 = mean
sigma = 0.4 = standard deviation


Let's find the z score when x = 1.82
z = (x - mu)/sigma
z = (1.82 - 2.62)/0.4
z = -2
This score is exactly 2 standard deviations below the mean.


The task of computing P(X > 1.82) is equivalent to finding P(Z > -2).


The empirical rule says roughly 95% of the normal distribution is within 2 standard deviations of the mean.


That means there is roughly 2.5% of the distribution in the left tail since (100%-95%)/2 = 2.5%
The remaining portion is then 100% - 2.5% = 97.5%


Or basically there's 95% in the middle and 2.5% in the right tail, so 95% + 2.5% = 97.5%
and P(Z > -2) = 0.975


Check out this diagram below
*[illustration Screenshot_105.png]


Answer: <font color=red>Approximately 97.5%</font>
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