Finding probability with mean and standard deviation normal distribution

Answer

finding probability with mean and standard deviation normal distribution

If you have the mean and standard deviation of a normally distributed data set, you may calculate the probability of a certain event.

You may calculate the z-score using them by using the formula z = (x – (mean)) / (standard deviation). With this score, you may look up the chance of that z-score occuring in the Standard Normal Distribution Tables.

Previously, we extensively covered on calculating the Z-VALUES. Click Here to see the calculations.

For Example:

​What is the probability that x is greater than 5.5 in a normally distributed data given that the mean is 8 and the standard deviation is 0.9.

Solution

$P(x>5.5)$

Calculating the Z-score

$z=\frac{x-\mu }{\delta }$

$For P(x>5.5) we have z=\frac{5.5-8}{0.9}$

=-2.7777778

rounding it up we get -2.78

checking the value of -2.78 on the Z-tables we have.

probability=0.0272

=0.0272

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