The finished inside diameter of a piston ring is normally distributed with a mean of 8 centimeters and a standard deviation of 0.02 centimeter. 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) What proportion of rings will have inside diameters exceeding 8.042 centimeters? (Round to four decimal places as needed.) (b) What is the probability that a piston ring will have an inside diameter between 7.94 and 8.06 centimeters? (Round to four decimal places as needed.) (c) Below what value of inside diameter will 15% of the piston rings fall? centimeters (Round to three decimal places as needed.)
The finished inside diameter of a piston ring is normally distributed with a mean of 8 centimeters and a standard deviation of 0.02 centimeter. 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) What proportion of rings will have inside diameters exceeding 8.042 centimeters? (Round to four decimal places as needed.) (b) What is the probability that a piston ring will have an inside diameter between 7.94 and 8.06 centimeters? (Round to four decimal places as needed.) (c) Below what value of inside diameter will 15% of the piston rings fall? centimeters (Round to three decimal places as needed.)
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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Transcribed Image Text:Areas under the Normal Curve
Areas under the Normal Curve
12 05 05
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.01
.02
.03
.04
-3.4
-3.3
-2.8 0.0026 0.0025
2
.05
.06
.07
0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
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
-3.1
0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016
0.0016 0.0015
0.0015 0.0014 0.0014 -2.9
0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8
-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 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250
0.0244
0.0239 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 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -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 0.0934 0.0918 0.0901 0.0885 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 0.1170 -1.1
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-0.9
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-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 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1
-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
.01
.02
.03
.04
.05
.06
.07
.08
.09
.08
.09
Z
.04
0.0003 0.0002 -3.4
0.0004 0.0003
-3.3
0.0005 0.0005 -3.2
0.0007 0.0007 -3.1
0.0010 0.0010 -3.0
0.0
0.0066 0.0064 -2.4
0.0087 0.0084 -2.3
0.0113 0.0110 -2.2
0.0146 0.0143 -2.1
0.0188 0.0183 -2.0
0.9 0.8159
1.0
0.8413
1.1 0.8643
1.2 0.8849
1.3 0.9032
1.4 0.9192
1.5 0.9332
2.1
2.2
.00
.01
.02
.03
.06
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.3 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
0.8186 0.8212 0.8238 0.8264 0.8289 0.8315
0.8340
0.8365 0.8389 0.9
0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1
0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
0.9345 0.9357 0.9370 0.9382 0.9394 0.9406
0.9418 0.9429 0.9441 1.5
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0,9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 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
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 0.9962 0.9963 0.9964 2.6
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
.05
.07
.08
.09
2
3.1
C
3.2
3.3
C
¡A
3.4
0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1
0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
Dr
2
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
2
Transcribed Image Text:The finished inside diameter of a piston ring is normally distributed with a mean of 8 centimeters and a standard
deviation of 0.02 centimeter. 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) What proportion of rings will have inside diameters exceeding 8.042 centimeters?
(Round to four decimal places as needed.)
(b) What is the probability that a piston ring will have an inside diameter between 7.94 and 8.06 centimeters?
(Round to four decimal places as needed.)
(c) Below what value of inside diameter will 15% of the piston rings fall?
centimeters
(Round to three decimal places as needed.)
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Step 1: Define the given data
VIEWStep 2: Obtain the proportion of rings will have inside diameters exceeding 8.042 centimeters
VIEWStep 3: Obtain the probability that a piston ring will have an inside diameter between 7.94 and 8.06 cm.
VIEWStep 4: Obtain the value of the inside diameter that the 15% of the piston rings fall
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