Problem 6-7 Wayback Cleaning Co.
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 128.225 NORMAL PROBABILITY CALCULATIONS
Std deviation of distribution 5
Desired x-value 120 Mean of distribution 1020
Calculated z-value -1.645 Std Dev of distribution 20
Probability of x, or less 0.04998 Desired x-value 1044
(X-axis) Probability Using Prob. of x, or less 0.88493
Desired x-values Equivalent – Z Values NORMS.DIST
88.225 -8.00 0.00000 Equivalent Probability Using Desired
89.225 -7.80 0.00000 Z Values NORM.DIST x-values
90.225 -7.60 0.00000 -4.00 0.00003 940
91.225 -7.40 0.00000 -3.60 0.00016 948
92.225 -7.20 0.00000 -3.20 0.00069 956
106.225 -4.40 0.00001 2.40 0.99180 1068
107.225 -4.20 0.00001 2.80 0.99744 1076
108.225 -4.00 0.00003 3.20 0.99931 1084
109.225 -3.80 0.00007 3.60 0.99984 1092
110.225 -3.60 0.00016 4.00 0.99997 1100
0.80
0.90
1.00
-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
NORMS.DIST
Mean of distribution 1020
Std Dev of distribution 20
Prob. of x, or less 0.88493
Equivalent Probability Using Desired
Z Values NORM.DIST x-values
93.225 -7.00 0.00000 -2.80 0.00256 964
94.225 -6.80 0.00000 -2.40 0.00820 972
95.225 -6.60 0.00000 -2.00 0.02275 980
96.225 -6.40 0.00000 -1.60 0.05480 988
97.225 -6.20 0.00000 -1.20 0.11507 996
100.225 -5.60 0.00000 0.00 0.50000 1020
101.225 -5.40 0.00000 0.40 0.65542 1028
102.225 -5.20 0.00000 0.80 0.78814 1036
103.225 -5.00 0.00000 1.20 0.88493 1044
104.225 -4.80 0.00000 1.60 0.94520 1052
105.225 -4.60 0.00000 2.00 0.97725 1060
-2.80 0.00256 964
-2.40 0.00820 972
-2.00 0.02275 980
-1.60 0.05480 988
-1.20 0.11507 996
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