Normal probabilities can be calculated using MINITAB. Let \(X\) have a normal distribution with mean 11.3 and standard deviation 5.7. The following steps yield the cumulative probability of 9.31 or smaller, or \(P(X \leq 9.31)\).

Output:

 Normal with mean \(=11.3000\) and standard deviation \(=5.70000\)
\[\begin{array}{rr}
x & P(X9.3100 & 0.3635 \end{array}\]
For this same normal distribution, find the probability

(a) of 8.493 or smaller;

(b) of 16.074 or smaller.

Data From Deviation 5.7

Dialog box: Calc > Probability Distribution > Normal Choose Cumulative Distribution. Choose Input constant and enter 9.31. Type 11.3 in Mean and 5.7 in standard deviation. Click OK.