Problem 6-9 Machined Part
Probability Calculations Using the Normal Distribution – Template
Enter data only in the shaded cells
This spreadsheet is designed to calculate the probability of values equal to, or less than, a desired x value,
given the mean and standard deviation of a normally distributed variable. It uses the cumulative normal distribution
Enter the mean of the distribution in shaded cell D8 and the standard deviation in shaded cell D9. below.
Enter the desired X-value in shaded cell D10, below. The calculated z-value and probability will be seen in D11 and D12.
Mean of distribution 11.9 11.9 11.9 NORMAL PROBABILITY CALCULATIONS
Std deviation of distribution 0.05 0.05 0.05
Desired x-value 12 11.95 11.83 Mean of distribution 1020
Calculated z-value 2.000 1.000 -1.400 Std Dev of distribution 20
Probability of x, or less 0.97725 0.84134 0.08076 Desired x-value 1044
Calculated z-value 1.20
(X-axis) Probability Using Prob. of x, or less 0.88493
Desired x-values Equivalent – Z Values NORMS.DIST
11.700 -4.00 0.00003 Equivalent Probability Using Desired
11.790 -2.20 0.01390 2.40 0.99180 1068
11.795 -2.10 0.01786 2.80 0.99744 1076
11.800 -2.00 0.02275 3.20 0.99931 1084
11.805 -1.90 0.02872 3.60 0.99984 1092
11.810 -1.80 0.03593 4.00 0.99997 1100
11.815 -1.70 0.04457
11.820 -1.60 0.05480
11.825 -1.50 0.06681
11.830 -1.40 0.08076
11.835 -1.30 0.09680
11.840 -1.20 0.11507
11.845 -1.10 0.13567
11.850 -1.00 0.15866
11.855 -0.90 0.18406
11.860 -0.80 0.21186
11.865 -0.70 0.24196
11.870 -0.60 0.27425
11.875 -0.50 0.30854
11.880 -0.40 0.34458
11.885 -0.30 0.38209
11.890 -0.20 0.42074
11.895 -0.10 0.46017
11.900 0.00 0.50000
11.905 0.10 0.53983
11.910 0.20 0.57926
11.915 0.30 0.61791
11.920 0.40 0.65542
11.925 0.50 0.69146
11.930 0.60 0.72575
11.935 0.70 0.75804
11.940 0.80 0.78814
11.945 0.90 0.81594
11.950 1.00 0.84134
11.955 1.10 0.86433
11.960 1.20 0.88493
11.965 1.30 0.90320
11.970 1.40 0.91924
11.975 1.50 0.93319
11.980 1.60 0.94520
11.985 1.70 0.95543
11.990 1.80 0.96407
11.995 1.90 0.97128
12.000 2.00 0.97725
12.005 2.10 0.98214
12.010 2.20 0.98610
12.015 2.30 0.98928
12.020 2.40 0.99180
12.025 2.50 0.99379
12.030 2.60 0.99534
12.035 2.70 0.99653
12.040 2.80 0.99744
12.045 2.90 0.99813
12.050 3.00 0.99865
12.055 3.10 0.99903
12.060 3.20 0.99931
12.065 3.30 0.99952
12.070 3.40 0.99966
12.075 3.50 0.99977
12.080 3.60 0.99984
12.085 3.70 0.99989
12.090 3.80 0.99993
12.095 3.90 0.99995
12.100 4.00 0.99997
-4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0-1.8-1.6-1.4-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
z-values
Cumulative Probability Function
Mean of distribution 1020
Std Dev of distribution 20
Desired x-value 1044
Calculated z-value 1.20
Prob. of x, or less 0.88493
Equivalent Probability Using Desired
2.40 0.99180 1068
2.80 0.99744 1076
3.20 0.99931 1084
3.60 0.99984 1092
4.00 0.99997 1100
11.705 -3.90 0.00005 Z Values NORM.DIST x-values
11.750 -3.00 0.00135 -0.80 0.21186 1004
11.755 -2.90 0.00187 -0.40 0.34458 1012
11.760 -2.80 0.00256 0.00 0.50000 1020
11.765 -2.70 0.00347 0.40 0.65542 1028
11.770 -2.60 0.00466 0.80 0.78814 1036
11.775 -2.50 0.00621 1.20 0.88493 1044
11.780 -2.40 0.00820 1.60 0.94520 1052
11.785 -2.30 0.01072 2.00 0.97725 1060
0.00 0.50000 1020
0.40 0.65542 1028
0.80 0.78814 1036
1.20 0.88493 1044
1.60 0.94520 1052