In a family with 2 children, the probability that all the children are girls is approximately 0.25. In a random sample of 1000 families with 2 children, what is the approximate probability that 200 or fewer will have 2 girls? Approximate a binomial distribution with a nomal distribution. E Click the icon to view the area under the standard nomal curve table. The probability that 200 or fewer families will have 2 girls is. (Round to four decimal places as needed.)

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0.4177
utand
Area
corresponding
to
have 2
2.
(Table Entries Represent the Area under the Standard Normal Curve from 0 to z, z20)
.07
0.0279
02
.03
0.0120
.00
.01
.04
.05
.06
.08
.09
0.0
0.0000
0.0040
0,0080
0,0160
0.0199
0.0239
0.0319
0.0359
0.1
0.0398
0.0438
0.0478
0.0517
0.0557
0.0596
0.0636
0.0675
0.0714
0.0753
0.2
0.0793
0.0832
0.0871
0.0910
0.0948
0.0987
0.1026
0.1064
0.1103
0.1141
0.1217
0.1591
0.3
0.1179
0.1255
0.1293
0.1331
0.1368
0.1406
0.1443
0.1480
0.1517
0.4
0.1554
0.1628
0.1664
0.1700
0.1736
0.1772
0.1808
0.1844
0.1879
0.5
0.1915
0.1950
0.1985
0.2019
0.2054
0.2088
0.2123
0.2157
0.2190
0.2224
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2422
0.2454
0.2486
0.2517
0.2549
0.7
0.2580
0.2611
0.2642
0.2673
0.2704
0.2734
0.2764
0.2794
0.2823
0.2852
0.8
0.2881
0.2910
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3133
0.9
0.3159
0.3186
0.3212
0.3238
0.3264
0.3289
0.3315
0.3340
0.3365
0.3389
1.0
0.3413
0.3438
0.3461
0.3485
0.3508
0.3531
0.3554
0.3577
0.3599
0.3621
1.1
0.3643
0.3665
0.3686
0.3708
0.3729
0.3749
0.3770
0.3790
0.3810
0.3830
1.2
0.3849
0.3869
0.3888
0.3907
0.3925
0.3944
0.3962
0.3980
0.3997
0.4015
13
0.4032
0.4049
0.4066
0.4082
0.4099
0.4115
0.4131
0.4147
0.4162
0.4177
1.4
0.4192
0.4207
0.4222
0.4236
0.4251
0.4265
0.4279
0.4292
0.4306
0.4319
1.5
0.4332
0.4345
0.4357
0.4429
0.4535
0.4370
0.4382
0.4394
0.4406
0.4418
0.4441
1.6
0,4452
0.4463
0,4474
0.4484
0.4495
0.4505
0.4515
0.4525
0.4545
1.7
0.4554
0.4564
0.4573
0.4582
0.4591
0,4599
0.4608
0.4616
0.4625
0.4633
1.8
0.4641
0.4649
0.4656
0.4664
0.4671
0.4678
0.4686
0.4693
0.4699
0.4706
1.9
0.4713
0.4719
0.4726
0.4744
0.4798
0.4732
0.4738
0.4750
0.4756
0.4761
0.4767
2.0
0.4772
0.4778
0.4783
0.4788
0.4793
0.4803
0.4808
0.4812
0.4817
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Transcribed Image Text:0.4177 utand Area corresponding to have 2 2. (Table Entries Represent the Area under the Standard Normal Curve from 0 to z, z20) .07 0.0279 02 .03 0.0120 .00 .01 .04 .05 .06 .08 .09 0.0 0.0000 0.0040 0,0080 0,0160 0.0199 0.0239 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.1217 0.1591 0.3 0.1179 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 13 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4429 0.4535 0.4370 0.4382 0.4394 0.4406 0.4418 0.4441 1.6 0,4452 0.4463 0,4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0,4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4744 0.4798 0.4732 0.4738 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4803 0.4808 0.4812 0.4817 Print Done Help me solve this Get more help - MacBook Air 吕0 F3 888 F2 D00 FA F5 F6 F7 F8 F10 #3 2$ & * 3 4 5 7 8 Y D F G H K
In a family with 2 children, the probability that all the children are girls is approximately 0.25. In a random sample of 1000 families with 2 children, what is the approximate probability that 200 or fewer will have 2 girls? Approximate a binomial
distribution with a normal distribution.
E Click the icon to view the area under the standard normal curve table.
The probability that 200 or fewer families will have 2 girls is-
(Round to four decimal places as needed.)
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Transcribed Image Text:In a family with 2 children, the probability that all the children are girls is approximately 0.25. In a random sample of 1000 families with 2 children, what is the approximate probability that 200 or fewer will have 2 girls? Approximate a binomial distribution with a normal distribution. E Click the icon to view the area under the standard normal curve table. The probability that 200 or fewer families will have 2 girls is- (Round to four decimal places as needed.) Clear all Check answer View instructor tip Help me solve this Get more help- MacBook Air F7 * F4 esc FI F2 % & delete # $ 8 2 3 4 E T. Y Q W tab K G S cops lock a>
Expert Solution
Step 1

Givenp=0.25sample size(n)=1000x~Binomial(n=1000,p=0.25)P(X=x)=(nx)×px×(1-p)n-x   ; x=0,1,...,n 

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