(a) Find the mean and the variance o² of X. = 4.6 (Type an integer or a decimal. Do not round.) 20.84 (Type an integer or a decimal. Do not round.) (b) Find the mean μ and the variance σ of the mean X for random samples of 36 cherry puffs. H = 4.6 (Type an integer or a decimal. Do not round.) =0.023 (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9. The probability is 0.9752 (Round to four decimal places as needed.)
(a) Find the mean and the variance o² of X. = 4.6 (Type an integer or a decimal. Do not round.) 20.84 (Type an integer or a decimal. Do not round.) (b) Find the mean μ and the variance σ of the mean X for random samples of 36 cherry puffs. H = 4.6 (Type an integer or a decimal. Do not round.) =0.023 (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9. The probability is 0.9752 (Round to four decimal places as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown.
x
P(X = x)
3
4
5
6
0.4
0.3
0.2
Complete parts (a) through (c) below.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
(a) Find the mean μ and the variance o² of X.
= 4.6 (Type an integer or a decimal. Do not round.)
²=0.84 (Type an integer or a decimal. Do not round.)
(b) Find the mean μx and the variance o✓ of the mean X for random samples of 36 cherry puffs.
H4.6 (Type an integer or a decimal. Do not round.)
0.023 (Round to three decimal places as needed.)
(c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9.
The probability is 0.9752
(Round to four decimal places as needed.)
Transcribed Image Text:الها
Areas under the Normal Curve
> >
2
.00
Areas under the Normal Curve
.01
.02
.03
.04
0.0129
0.4443
.01
.02
.04
z
.00
.01
.02
.03
.04
.05
.06
.07
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005
0.0010 0.0009
-3.1
0.0009 0.0009 0.0008 0.0008 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031
0.0030 0.0029 0.0028 0.0027 0.0026 -2.7
-2.6
0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5
-2.4 0.0082
0.0078 0.0075
0.0080
0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3
-2.2 0.0139 0.0136 0.0132
0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2
-2.1 0.0179 0.0174 0.0170 0.0166
0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.1
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0
-1.9
0.0281
0.0287
0.0268
0.0274
0.0262 0.0256 0.0250
0.0239
0.0244
0.0233 -1.9
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8
-1.7
0.0436 0.0427 0.0418
0.0446
0.0409 0.0401
0.0384 0.0375 0.0367
0.0392
-1.7
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3 0.0968 0.0951
0.0918 0.0901 0.0885
0.0934
0.0869 0.0853 0.0838 0.0823 -1.3
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.2
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210
0.1190
-1.1
0.1170
-1.0
0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
0.1841
0.1788 0.1762
0.1814
0.1736 0.1711 0.1685 0.1660
-0.9
0.1611 -0.9
0.1635
-0.8 0.2119
0.2061 0.2033 0.2005
0.2090
0.1977 0.1949 0.1922 0.1894
-0.8
0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.3
-0.2 0.4207
0.4090
0.4013
0.3974
0.4168
0.3897
0.4129
0.3859 -0.2
0.4052
0.3936
0.4602
0.4483
-0.1
0.4562
0.4364
0.4522
0.4325 0.4286
0.4404
-0.1
0.4247
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.00
.03
.05
.06
.07
.08
.08
.09
2
0.0003 0.0002 -3.4
0.0004 0.0003 -3.3
0.0005 0.0005 -3.2
0.0008 0.0007 0.0007 -3.1
0.0011 0.0010 0.0010 -3.0
0.0015 0.0014
0.3
0.0021 0.0020
0.0014 -2.9
0.0019 -2.8
1.6
1.7
1.8
1.9
2.1
1
+
2.9 0.9981
3.0
3.1
.07
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881
0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159
0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
0.8643
1.1
0.8665 0.8686 0.8708
0.8749
0.8729
0.8770 0.8790 0.8810
1.1
0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
0.9463
0.9452
0.9474 0.9484 0.9495 0.9505 0.9515
1.6
0.9525 0.9535 0.9545
0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
0.9649 0.9656
0.9641
0.9664 0.9671
0.9693
0.9678 0.9686
0.9706
0.9699
1.8
0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911
0.9913 0.9916 2.3
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961
0.9963 0.9964
0.9962
2.6
0.9965
2.7
0.9966 0.9967 0.9968
0.9970
0.9969
0.9971 0.9972 0.9973 0.9974 2.7
回 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
0.9982 0.9982 0.9983 0.9984 0.9984 0.9985
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989
0.9990 0.9991
.05
.06
.08
.09
0.5359 0.0
0.5753 0.1
0.6141 0.2
0.9985 0.9986 0.9986 2.9
A
3.2
3.3
A 3.4
0.9991 0.9991 0.9992 0.9992 0.9992
0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
0.9989 0.9990 0.9990 3.0
0.9992 0.9993 0.9993 3.1
2
0.9995 0.9995
0.9997 0.9997
.00
.01
0.9995 0.9996
0.9997 0.9997
.02
.03
0.9996
0.9996
0.9997
0.9997
0.9996
0.9997
.04
.05
.06
0.9996 0.9996
0.9997 0.9997
.07
.08
0.9997
0.9998
.09
3.3
3.4
.09
2
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