Question

Use Excel functions to find the following probability of Normal distribution

a.) P (X > 70) when X ~ N (65, 10)

b.) P(20 < X < 40) when X ~ N (32, 12)

Answer 1

a)   P (X > 70) = 1 -  P (X < 70) ----(1)

Here mean = 65 and standard deviation = 10

We want to find P(X < 70)

Let's use "==NORMDIST(x, mean, standard_dev, cumulative)  this excel command to find the less than normal probabilities.

P(X < 70) = "=NORMDIST(70, 65, 10,1)" = 0.691462

Plug this value in equation (1), we get

P(X > 70) = 1 -  P(X < 70) = 1 -  0.691462 = 0.308538

b) b.) P(20 < X < 40) when X ~ N (32, 12)

P(20 < X < 40) = P( X < 40) -  P( X < 20)......(2)

Let P( X < 40) = "=NORMDIST(40, 65, 10,1)" = 0.00621

Let P( X < 20)=NORMDIST(20, 65, 10,1) = 0.0000034

Plug these values in equation 2, we get

P(20 < X < 40) =  0.00621 -  0.0000034 = 0.006206268