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# Standard Normal Distribution Function

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## Quick Reference

The table gives the values of Φ(z)=P(Z < z), where Z has a normal distribution with mean 0 and variance 1.

Φ(z)

z0123456789123456789

0.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.53594812162024283236

0.1.5398.5438.5478.5517.5557.5596.5636.5675.5714.57534812162024283236

0.2.5793.5832.5871.5910.5948.5987.6026.6064.6103.61414812151923273135

0.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.65174711151922263034

0.4.6554.6591.6628.6664.6700.6736.6772.6808.6844.68794711141822252932

0.5.6915.6950.6985.7019.7054.7088.7123.7157.7190.72243710141720242731

0.6.7257.7291.7324.7357.7389.7422.7454.7486.7517.75493710131619232629

0.7.7580.7611.7642.7673.7704.7734.7764.7794.7823.7852369121518212427

0.8.7881.7910.7939.7967.7995.8023.8051.8078.8106.8133358111416192225

0.9.8159.8186.8212.8238.8264.8289.8315.8340.8365.8389358101315182023

1.0.8413.8438.8461.8485.8508.8531.8554.8577.8599.862125791214161921

1.1.8643.8665.8686.8708.8729.8749.8770.8790.8810.883024681012141618

1.2.8849.8869.8888.8907.8925.8944.8962.8980.8997.90152467911131517

1.3.9032.9049.9066.9082.9099.9115.9131.9147.9162.91772356810111314

Example: Φ(0.657)=0.7422+0.0023=0.7445

Φ(z)

z0123456789123456789

1.4.9192.9207.9222.9236.9251.9265.9279.9292.9306.9319134678101113

1.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.944112456781011

1.6.9452.9463.9474.9484.9495.9505.9515.9525.9535.9545123456789

1.7.9554.9564.9573.9582.9591.9599.9608.9616.9625.9633123445678

1.8.9641.9649.9656.9664.9671.9678.9686.9693.9699.9706112344566

1.9.9713.9719.9726.9732.9738.9744.9750.9756.9761.9767112234455

2.0.9772.9778.9783.9788.9793.9798.9803.9808.9812.9817011223344

2.1.9821.9826.9830.9834.9838.9842.9846.9850.9854.9857011222334

2.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.9890011122233

2.3.9893.9896.9898.9901.9904.9906.9909.9911.9913.9916011112222

2.4.9918.9920.9922.9924.9927.9929.9931.9932.9934.9936001111122

2.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.9952000111111

2.6.9953.9955.9956.9957.9958.9960.9961.9962.9963.9964000011111

2.7.9965.9966.9967.9968.9969.9970.9971.9972.9973.9974000001111

2.8.9974.9975.9976.9977.9977.9978.9979.9979.9980.9981000000011

2.9.9981.9982.9982.9983.9984.9984.9985.9985.9986.9986000000000

Example: Φ(1.846)=0.9671+0.0004=0.9675

From A Dictionary of Statistics in Oxford Reference.

Subjects: Probability and Statistics.

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