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.
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.
Calculating the Z-score
rounding it up we get -2.78
checking the value of -2.78 on the Z-tables we have.