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70% of all new-car purchases by families. Suppose five families have decided to buy a new car. a. What is the probability that in exactly two of the five families the husband will exert the primary influence in choosing the make of a car? b. What is the probability that the husband will select the make of car in all five families?

70% of all new-car purchases by families. Suppose five families have decided to buy a new car. a. What is the probability that in exactly two of the five families the husband will exert the primary influence in choosing the make of a car? b. What is the probability that the husband will select the make of car in all five families?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 17E
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Question

2. A study concerning the relative influence of husbands and wives in consumer
purchasing, which appeared in recent issue of Time Magazine, reported that
husband exerts the primary influence in selecting the make of a new automobile
in about 70% of all new-car purchases by families. Suppose five families have
decided to buy a new car.


a. What is the probability that in exactly two of the five families the husband
will exert the primary influence in choosing the make of a car?
b. What is the probability that the husband will select the make of car in all five
families?
c. What is the probability that the husband will exert the primary influence in
choosing the make of a car in at least three of the five families? Use Binomial Table given
below. 

 

 

 

Tabulated values are P(X < k) = Ep(x,). (Values are rounded to four decimal places.) X=0 n = 5 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9510 0.7738 0.5905 0.3277 0.2373 0.1681 0.0778 0.0313 0.0102 0.0024 0.0010 0.0003 0.0000 0.0000 0.0000 1 0.9990 0.9774 0.9185 0.7373 0.6328 0.5282 0.3370 0.1875 0.0870 0.0308 0.0156 0.0067 0.0005 0.0000 0.0000 1.0000 0.9988 0.9914 0.9421 0.8965 0.8369 0.6826 0.5000 0.3174 0.1631 0.1035 0.0579 0.0086 0.0012 0.0000 1.0000 1.0000 0.9995 0.9933 0.9844 0.9692 0.9130 0.8125 0.6630 0.4718 0.3672 0.2627 0.0815 0.0226 0.0010 1.0000 1.0000 1.0000 0.9997 0.9990 0.9976 0.9898 0.9688 0.9222 0.8319 0.7627 0.6723 0.4095 0.2262 0.0490 n = 6 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9415 0.7351 0.5314 0.2621 0.1780 0.1176 0.0467 0.0156 0.0041 0.0007 0.0002 0.0001 0.0000 0.0000 0.0000 1 0.9985 0.9672 0.8857 0.6554 0.5339 0.4202 0.2333 0.1094 0.0410 0.0109 0.0046 0.0016 0.0001 0.0000 0.0000 1.0000 0.9978 0.9842 0.9011 0.8306 0.7443 0.5443 0.3438 0.1792 0.0705 0.0376 0.0170 0.0013 0.0001 0.0000 1.0000 0.9999 0.9987 0.9830 0.9624 0.9295 0.8208 0.6563 0.4557 0.2557 0.1694 0.0989 0.0159 0.0022 0.0000 4 1.0000 1.0000 0.9999 0.9984 0.9954 0.9891 0.9590 0.8906 0.7667 0.5798 0.4661 0.3446 0.1143 0.0328 0.0015 1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9959 0.9844 0.9533 0.8824 0.8220 0.7379 0.4686 0.2649 0.0585 n = 7 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9321 0.6983 0.4783 0.2097 0.1335 0.0824 0.0280 0.0078 0.0016 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 1 0.9980 0.9556 0.8503 0.5767 0.4449 0.3294 0.1586 0.0625 0.0188 0.0038 0.0013 0.0004 0.0000 0.0000 0.0000 1.0000 0.9962 0.9743 0.8520 0.7564 0.6471 0.4199 0.2266 0.0963 0.0288 0.0129 0.0047 0.0002 0.0000 0.0000 1.0000 0.9998 0.9973 0.9667 0.9294 0.8740 0.7102 0.5000 0.2898 0.1260 0.0706 0.0333 0.0027 0.0002 0.0000 1.0000 1.0000 0.9998 0.9953 0.9871 0.9712 0.9037 0.7734 0.5801 0.3529 0.2436 0.1480 0.0257 0.0038 0.0000 1.0000 1.0000 1.0000 0.9996 0.9987 0.9962 0.9812 0.9375 0.8414 0.6706 0.5551 0.4233 0.1497 0.0444 0.0020 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9984 0.9922 0.9720 0.9176 0.8665 0.7903 0.5217 0.3017 0.0679 (Continued) 6.
Transcribed Image Text:Tabulated values are P(X < k) = Ep(x,). (Values are rounded to four decimal places.) X=0 n = 5 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9510 0.7738 0.5905 0.3277 0.2373 0.1681 0.0778 0.0313 0.0102 0.0024 0.0010 0.0003 0.0000 0.0000 0.0000 1 0.9990 0.9774 0.9185 0.7373 0.6328 0.5282 0.3370 0.1875 0.0870 0.0308 0.0156 0.0067 0.0005 0.0000 0.0000 1.0000 0.9988 0.9914 0.9421 0.8965 0.8369 0.6826 0.5000 0.3174 0.1631 0.1035 0.0579 0.0086 0.0012 0.0000 1.0000 1.0000 0.9995 0.9933 0.9844 0.9692 0.9130 0.8125 0.6630 0.4718 0.3672 0.2627 0.0815 0.0226 0.0010 1.0000 1.0000 1.0000 0.9997 0.9990 0.9976 0.9898 0.9688 0.9222 0.8319 0.7627 0.6723 0.4095 0.2262 0.0490 n = 6 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9415 0.7351 0.5314 0.2621 0.1780 0.1176 0.0467 0.0156 0.0041 0.0007 0.0002 0.0001 0.0000 0.0000 0.0000 1 0.9985 0.9672 0.8857 0.6554 0.5339 0.4202 0.2333 0.1094 0.0410 0.0109 0.0046 0.0016 0.0001 0.0000 0.0000 1.0000 0.9978 0.9842 0.9011 0.8306 0.7443 0.5443 0.3438 0.1792 0.0705 0.0376 0.0170 0.0013 0.0001 0.0000 1.0000 0.9999 0.9987 0.9830 0.9624 0.9295 0.8208 0.6563 0.4557 0.2557 0.1694 0.0989 0.0159 0.0022 0.0000 4 1.0000 1.0000 0.9999 0.9984 0.9954 0.9891 0.9590 0.8906 0.7667 0.5798 0.4661 0.3446 0.1143 0.0328 0.0015 1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9959 0.9844 0.9533 0.8824 0.8220 0.7379 0.4686 0.2649 0.0585 n = 7 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9321 0.6983 0.4783 0.2097 0.1335 0.0824 0.0280 0.0078 0.0016 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 1 0.9980 0.9556 0.8503 0.5767 0.4449 0.3294 0.1586 0.0625 0.0188 0.0038 0.0013 0.0004 0.0000 0.0000 0.0000 1.0000 0.9962 0.9743 0.8520 0.7564 0.6471 0.4199 0.2266 0.0963 0.0288 0.0129 0.0047 0.0002 0.0000 0.0000 1.0000 0.9998 0.9973 0.9667 0.9294 0.8740 0.7102 0.5000 0.2898 0.1260 0.0706 0.0333 0.0027 0.0002 0.0000 1.0000 1.0000 0.9998 0.9953 0.9871 0.9712 0.9037 0.7734 0.5801 0.3529 0.2436 0.1480 0.0257 0.0038 0.0000 1.0000 1.0000 1.0000 0.9996 0.9987 0.9962 0.9812 0.9375 0.8414 0.6706 0.5551 0.4233 0.1497 0.0444 0.0020 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9984 0.9922 0.9720 0.9176 0.8665 0.7903 0.5217 0.3017 0.0679 (Continued) 6.
n = 8 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9227 0.6634 0.4305 0.1678 0.1001 0.0576 0.0168 0.0039 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9973 0.9428 0.8131 0.5033 0.3671 0.2553 0.1064 0.0352 0.0085 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000 0.9999 0.9942 0.9619 0.7969 0.6785 0.5518 0.3154 0.1445 0.0498 0.0113 0.0042 0.0012 0.0000 0.0000 0.0000 1.0000 0.9996 0.9950 0.9437 0.8862 0.8059 0.5941 0.3633 0.1737 0.0580 0.0273 0.0104 0.0004 0.0000 0.0000 4 1.0000 1.0000 0.9996 0.9896 0.9727 0.9420 0.8263 0.6367 0.4059 0.1941 0.1138 0.0563 0.0050 0.0004 0.0000 1.0000 1.0000 1.0000 0.9988 0.9958 0.9887 0.9502 0.8555 0.6846 0.4482 0.3215 0.2031 0.0381 0.0058 0.0001 6 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9915 0.9648 0.8936 0.7447 0.6329 0.4967 0.1869 0.0572 0.0027 7 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961 0.9832 0.9424 0.8999 0.8322 0.5695 0.3366 0.0773 n = 9 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9135 0.6302 0.3874 0.1342 0.0751 0.0404 0.0101 0.0020 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9966 0.9288 0.7748 0.4362 0.3003 0.1960 0.0705 0.0195 0.0038 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.9999 0.9916 0.9470 0.7382 0.6007 0.4628 0.2318 0.0898 0.0250 0.0043 0.0013 0.0003 0.0000 0.0000 0.0000 3 1.0000 0.9994 0.9917 0.9144 0.8343 0.7297 0.4826 0.2539 0.0994 0.0253 0.0100 0.0031 0.0001 0.0000 0.0000 4 1.0000 1.0000 0.9991 0.9804 0.9511 0.9012 0.7334 0.5000 0.2666 0.0988 0.0489 0.0196 0.0009 0.0000 0.0000 1.0000 1.0000 0.9999 0.9969 0.9900 0.9747 0.9006 0.7461 0.5174 0.2703 0.1657 0.0856 0.0083 0.0006 0.0000 1.0000 1.0000 1.0000 0.9997 0.9987 0.9957 0.9750 0.9102 0.7682 0.5372 0.3993 0.2618 0.0530 0.0084 0.0001 7 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9962 0.9805 0.9295 0.8040 0.6997 0.5638 0.2252 0.0712 0.0034 8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9980 0.9899 0.9596 0.9249 0.8658 0.6126 0.3698 0.0865
Transcribed Image Text:n = 8 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9227 0.6634 0.4305 0.1678 0.1001 0.0576 0.0168 0.0039 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9973 0.9428 0.8131 0.5033 0.3671 0.2553 0.1064 0.0352 0.0085 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000 0.9999 0.9942 0.9619 0.7969 0.6785 0.5518 0.3154 0.1445 0.0498 0.0113 0.0042 0.0012 0.0000 0.0000 0.0000 1.0000 0.9996 0.9950 0.9437 0.8862 0.8059 0.5941 0.3633 0.1737 0.0580 0.0273 0.0104 0.0004 0.0000 0.0000 4 1.0000 1.0000 0.9996 0.9896 0.9727 0.9420 0.8263 0.6367 0.4059 0.1941 0.1138 0.0563 0.0050 0.0004 0.0000 1.0000 1.0000 1.0000 0.9988 0.9958 0.9887 0.9502 0.8555 0.6846 0.4482 0.3215 0.2031 0.0381 0.0058 0.0001 6 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9915 0.9648 0.8936 0.7447 0.6329 0.4967 0.1869 0.0572 0.0027 7 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961 0.9832 0.9424 0.8999 0.8322 0.5695 0.3366 0.0773 n = 9 k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0.9135 0.6302 0.3874 0.1342 0.0751 0.0404 0.0101 0.0020 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9966 0.9288 0.7748 0.4362 0.3003 0.1960 0.0705 0.0195 0.0038 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.9999 0.9916 0.9470 0.7382 0.6007 0.4628 0.2318 0.0898 0.0250 0.0043 0.0013 0.0003 0.0000 0.0000 0.0000 3 1.0000 0.9994 0.9917 0.9144 0.8343 0.7297 0.4826 0.2539 0.0994 0.0253 0.0100 0.0031 0.0001 0.0000 0.0000 4 1.0000 1.0000 0.9991 0.9804 0.9511 0.9012 0.7334 0.5000 0.2666 0.0988 0.0489 0.0196 0.0009 0.0000 0.0000 1.0000 1.0000 0.9999 0.9969 0.9900 0.9747 0.9006 0.7461 0.5174 0.2703 0.1657 0.0856 0.0083 0.0006 0.0000 1.0000 1.0000 1.0000 0.9997 0.9987 0.9957 0.9750 0.9102 0.7682 0.5372 0.3993 0.2618 0.0530 0.0084 0.0001 7 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9962 0.9805 0.9295 0.8040 0.6997 0.5638 0.2252 0.0712 0.0034 8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9980 0.9899 0.9596 0.9249 0.8658 0.6126 0.3698 0.0865
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