Cellurific Battery Life-Reliability
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.
Part a (find 1 – prob) Part b
Mean of distribution 1100 1100 NORMAL PROBABILITY CALCULATIONS
Std deviation of distribution 60 60
Calculated z-value -1.75
(X-axis) Probability Using
Prob. of x, or less 0.04006
Desired x-values
Equivalent – Z Values NORM.DIST
860 -4.00 0.00003 Equivalent Probability Using Desired
866 -3.90 0.00005 Z Values NORM.DIST x-values
872 -3.80 0.00007 -4.00 0.00003 860
878 -3.70 0.00011 -3.60 0.00016 884
884 -3.60 0.00016 -3.20 0.00069 908
890 -3.50 0.00023 -2.80 0.00256 932
896 -3.40 0.00034 -2.40 0.00820 956
938 -2.70 0.00347 0.40 0.65542 1124
944 -2.60 0.00466 0.80 0.78814 1148
950 -2.50 0.00621 1.20 0.88493 1172
956 -2.40 0.00820 1.60 0.94520 1196
962 -2.30 0.01072 2.00 0.97725 1220
968 -2.20 0.01390 2.40 0.99180 1244
974 -2.10 0.01786 2.80 0.99744 1268
980 -2.00 0.02275 3.20 0.99931 1292
986 -1.90 0.02872 3.60 0.99984 1316
992 -1.80 0.03593 4.00 0.99997 1340
998 -1.70 0.04457
1004 -1.60 0.05480
1010 -1.50 0.06681
1016 -1.40 0.08076
1076 -0.40 0.34458
1082 -0.30 0.38209
1088 -0.20 0.42074
1094 -0.10 0.46017
1100 0.00 0.50000
1106 0.10 0.53983
1112 0.20 0.57926
1118 0.30 0.61791
1124 0.40 0.65542
1130 0.50 0.69146
1136 0.60 0.72575
1142 0.70 0.75804
1148 0.80 0.78814
1154 0.90 0.81594
1160 1.00 0.84134
1166 1.10 0.86433
1172 1.20 0.88493
1178 1.30 0.90320
1244 2.40 0.99180
1250 2.50 0.99379
1256 2.60 0.99534
1262 2.70 0.99653
1268 2.80 0.99744
1274 2.90 0.99813
1280 3.00 0.99865
1286 3.10 0.99903
1292 3.20 0.99931
1298 3.30 0.99952
1304 3.40 0.99966
1310 3.50 0.99977
1316 3.60 0.99984
1322 3.70 0.99989
1328 3.80 0.99993
1334 3.90 0.99995
1340 4.00 0.99997
0.00
0.10
0.20
0.70
0.80
0.90
1.00
-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Cumulative Probability
z-values
Cumulative Probability Function
Desired x-value 1200 995 Mean of distribution 1100
Cellurific Battery Life-Reliability
X-value Calculations Given Probabilities Using the Inverse Normal Distribution
This spreadsheet is designed to calculate the X-value based on probability of values equal to, or less than a desired x value,
of a normally distributed variable. It requires input of a known mean and standard deviation and uses the inverse of the cumulative normal distribution
Enter the mean of the distribution in cell D10 and the standard deviation in cell D11, below. Enter the desired probability in cell D12, and the calculated x-value will be seen in D13.
Mean of distribution 1100
Std Dev of distribution 60
Calculated x-values Probability Reliability – 1-P 920 0.00135
860 0.00003 0.99997 980 0.02275
866 0.00005 0.99995 1040 0.15866
872 0.00007 0.99993 1100 0.50000
878 0.00011 0.99989 1160 0.84134
884 0.00016 0.99984 1160 0.84134
932 0.00256 0.99744
938 0.00347 0.99653
944 0.00466 0.99534
950 0.00621 0.99379
956 0.00820 0.99180
962 0.01072 0.98928
968 0.01390 0.98610
974 0.01786 0.98214
980 0.02275 0.97725
986 0.02872 0.97128
992 0.03593 0.96407
998 0.04457 0.95543
1004 0.05480 0.94520
1070 0.30854 0.69146
1076 0.34458 0.65542
1082 0.38209 0.61791
1088 0.42074 0.57926
1094 0.46017 0.53983
1100 0.50000 0.50000
1106 0.53983 0.46017
1112 0.57926 0.42074
1118 0.61791 0.38209
1124 0.65542 0.34458
1130 0.69146 0.30854
1136 0.72575 0.27425
1142 0.75804 0.24196
1148 0.78814 0.21186
1154 0.81594 0.18406
1160 0.84134 0.15866
1166 0.86433 0.13567
1172 0.88493 0.11507
1178 0.90320 0.09680
1184 0.91924 0.08076
1256 0.99534 0.00466
1262 0.99653 0.00347
1268 0.99744 0.00256
1274 0.99813 0.00187
1280 0.99865 0.00135
1286 0.99903 0.00097
1292 0.99931 0.00069
1298 0.99952 0.00048
1304 0.99966 0.00034
1310 0.99977 0.00023
0.700
0.800
0.900
1.000
Reliability Curve
Probability of X or less
1316 0.99984 0.00016
1322 0.99989 0.00011
1328 0.99993 0.00007
1334 0.99995 0.00005
1340 0.99997 0.00003
Cellurific Battery Life-Reliability
Z and X-value Calculations Given Probabilites, Using the Inverse Normal Distribution – Template
This spreadsheet is designed to calculate the z-value based on probability of values equal to, or less than,
an equivalent x-value of a normally distributed variable. It uses the inverse of the cumulative normal distribution.
Enter the desired probability of the Z-value or less in the shaded cell D8, below.
The calculated z-value will be seen in cell D9.
Calculated
Equivalent
Probability Z Values x-values
0.00003 -4.00 860
0.00005 -3.90 866
0.00007 -3.80 872
0.00011 -3.70 878
0.00016 -3.60 884
0.00023 -3.50 890
0.00034 -3.40 896
0.00048 -3.30 902
0.00069 -3.20 908
0.00097 -3.10 914
0.00135 -3.00 920
0.00187 -2.90 926
0.00256 -2.80 932
0.03593 -1.80 992
0.04457 -1.70 998
0.05480 -1.60 1004
0.06681 -1.50 1010
0.08076 -1.40 1016
0.09680 -1.30 1022
0.11507 -1.20 1028
0.13567 -1.10 1034
0.15866 -1.00 1040
0.18406 -0.90 1046
0.21186 -0.80 1052
0.24196 -0.70 1058
0.27425 -0.60 1064
0.30854 -0.50 1070
0.34458 -0.40 1076
0.38209 -0.30 1082
0.42074 -0.20 1088
0.46017 -0.10 1094
0.50000 0.00 1100
0.53983 0.10 1106
0.57926 0.20 1112
0.61791 0.30 1118
0.65542 0.40 1124
0.69146 0.50 1130
0.93319 1.50 1190
0.94520 1.60 1196
0.95543 1.70 1202
0.96407 1.80 1208
0.97128 1.90 1214
0.97725 2.00 1220
0.98214 2.10 1226
0.98610 2.20 1232
0.00
1.00
2.00
3.00
4.00
5.00
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000
Z Values vs. Probability
Z Values
0.98928 2.30 1238
0.99180 2.40 1244
0.99379 2.50 1250
0.99534 2.60 1256
0.99653 2.70 1262
0.99984 3.60 1316
0.99989 3.70 1322
0.99993 3.80 1328
0.99995 3.90 1334
0.99997 4.00 1340