In normal distribution standard deviation will be one and mean will be greater than zero, where in standard normal distribution mean will be zero and standard deviation will be one.
We can very well convert normal distribution to standard/Z distribution with below formula.Because Z table is very easy to find the probability area.
We have normally distributed data with mean 20 and standard deviation 5.
Now let’s solve below problems.
What is the probability that temperature will be less than 25 degrees P(x<25).
What is the probability that temperature will be greater than 18 degrees P(x>18).
What is the probability that temperature will be P(18<X<25).
P(x<25):
First we need to convert the x value in to Z score, we already seen the formula above, now lets derive the formula.
As per the Z table P(x<25) is 0.841345 or 84.1345%.(P(Z=1) = 0.3413 we need to include the area of left side also so P(Z<1)=0.3413+0.5)
P(x>18)
We again need to convert x value to Z value
As per the Z table P(x>18) is 0.655422 or 65.5422%.
Z table from http://www.z-table.com/
Data and Machine by viswateja 