Calculate the probabilities for the variable Z, which has the standard normal distribution given below.1. Calculate the probability that the variable Z is greater than 1.87. P (Z> 1.87) standard normal table.00.01.02.03.04.05.06.07.08.090.05000.5040.50805120.5160.5199.5239.5279.5319.53590.1.5398.5438557855175557.5596.5636.5675.571457530.2.5793.5832587159105948.5987.6026.6064.610361410.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.65170.4.6554.6591.6628.6664.67006736.67726808.6844.68790.5.6915.6950.69857019.70547088.71237157.7190.72240.67257.7291.7324.735773897422.7454.7486.7517.75490.7758076117642767377047734.77647794.7823.78520.87881.79107939.796779958023.8051.8078.8106.81330.9.815981868212.82388264.82898315.83408365.83891.084138438.8461.84858508.8531.8554.8577.8599.86211.186438665868687088729874987708790.8810.88301.2884988698888.89078925.8944.8962.8980.8997.90151.390329049906690829099.9115.91319147.9162.91771.4919292079222.92369251926592799292.9306.93191.5933293459357937093829394940694189429.94411.69452946394749484949595059515.9525953595451.795549564957395829591.959996089616962596331.896419649965696649671.9678.96869693.969997061.9971397199726973297389744.97509756.976197672.097729778978397889793979898039808.9812.98172.1.982198269830.98349838984298469850.985498572.29861986498689871.9875987898819884988798902.39893989698989901990499069909991199132.49918.992099229925991699279929993199322.59938.994099349936994199439945994699489949995199522.69953.99559956.9957995999609961996299632.7996599669967.99689964.99699970.997199722.899749975.997699739974.99779977.9978199792.99981997999809981.9982.99829983998499849985998599863.09987.9987.9987998899889986998999890080

we have given that standard normal distribution X~N(0 , 1)

Answered: Calculate the probabilities for the…

Calculate the probabilities for the variable Z, which has the standard normal distribution given below. 1. Calculate the probability that the variable Z is greater than 1.87. P (Z> 1.87)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Calculate the probabilities for the variable Z, which has the standard normal distribution given below.
1. Calculate the probability that the variable Z is greater than 1.87. P (Z> 1.87)

standard normal table
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
5000
.5040
.5080
5120
.5160
.5199
.5239
.5279
.5319
.5359
0.1
.5398
.5438
5578
5517
5557
.5596
.5636
.5675
.5714
5753
0.2
.5793
.5832
5871
5910
5948
.5987
.6026
.6064
.6103
6141
0.3
.6179
.6217
.6255
.6293
.6331
.6368
.6406
.6443
.6480
.6517
0.4
.6554
.6591
.6628
.6664
.6700
6736
.6772
6808
.6844
.6879
0.5
.6915
.6950
.6985
7019
.7054
7088
.7123
7157
.7190
.7224
0.6
7257
.7291
.7324
.7357
7389
7422
.7454
.7486
.7517
.7549
0.7
7580
7611
7642
7673
7704
7734
.7764
7794
.7823
.7852
0.8
7881
.7910
7939
.7967
7995
8023
.8051
.8078
.8106
.8133
0.9
.8159
8186
8212
.8238
8264
.8289
8315
.8340
8365
.8389
1.0
8413
8438
.8461
.8485
8508
.8531
.8554
.8577
.8599
.8621
1.1
8643
8665
8686
8708
8729
8749
8770
8790
.8810
.8830
1.2
8849
8869
8888
.8907
8925
.8944
.8962
.8980
.8997
.9015
1.3
9032
9049
9066
9082
9099
.9115
.9131
9147
.9162
.9177
1.4
9192
9207
9222
.9236
9251
9265
9279
9292
.9306
.9319
1.5
9332
9345
9357
9370
9382
9394
9406
9418
9429
.9441
1.6
9452
9463
9474
9484
9495
9505
9515
.9525
9535
9545
1.7
9554
9564
9573
9582
9591
.9599
9608
9616
9625
9633
1.8
9641
9649
9656
9664
9671
.9678
.9686
9693
.9699
9706
1.9
9713
9719
9726
9732
9738
9744
.9750
9756
.9761
9767
2.0
9772
9778
9783
9788
9793
9798
9803
9808
.9812
.9817
2.1
.9821
9826
9830
.9834
9838
9842
9846
9850
.9854
9857
2.2
9861
9864
9868
9871
.9875
9878
9881
9884
9887
9890
2.3
9893
9896
9898
9901
9904
9906
9909
9911
9913
2.4
9918
.9920
9922
9925
9916
9927
9929
9931
9932
2.5
9938
.9940
9934
9936
9941
9943
9945
9946
9948
9949
9951
9952
2.6
9953
.9955
9956
.9957
9959
9960
9961
9962
9963
2.7
9965
9966
9967
.9968
9964
.9969
9970
.9971
9972
2.8
9974
9975
.9976
9973
9974
.9977
9977
.9978
19979
2.9
9981
9979
9980
9981
.9982
.9982
9983
9984
9984
9985
9985
9986
3.0
9987
.9987
.9987
9988
9988
9986
9989
9989
0080

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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