VCU STAT 210 - Test 4 - Solutions A-C(4) (4 pages)

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Test 4 - Solutions A-C(4)



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Test 4 - Solutions A-C(4)

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4
School:
Virginia Commonwealth University
Course:
Stat 210 - Basic Practice of Statistics
Basic Practice of Statistics Documents
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STAT 210 TEST 4 SOLUTIONS Version A 1 0 zero The probability that a normal variable is exactly equal to any value is zero 2 B C and D The Z distribution and all t distributions all have a bell shape a mean of zero and no unusual features The only difference between the Z and all t distributions is that they have different standard deviations 3 A A sampling distribution is the distribution of all values taken by a statistic in a large number of simple random samples of the same size from the same population 4 0 zero The mean of the standard normal Z distribution is zero 5 Top 1 32 implies find x such that P X x 0 0132 1 0 0132 0 9868 look up p 9868 in the body of the table find z 2 22 So x z 52 8 2 22 10 3 52 8 22 866 75 666 years old On the calculator invNorm 0 9868 52 8 10 3 75 669 years old 6 P X 24 P Z 24 52 8 10 3 P Z 2 80 0 0026 On the calculator normalcdf 1E99 24 52 8 10 3 0 0026 7 P X 46 P Z 46 52 8 10 3 P Z 0 66 1 P Z 0 66 1 0 2546 0 7454 On the calculator normalcdf 46 1E99 52 8 10 3 0 7454 8 P 28 X 37 P 37 52 8 Z 28 52 8 10 3 10 3 P 2 41 Z 1 53 P Z 1 53 P Z 2 41 0 0630 0 0080 0 0550 On the calculator normalcdf 28 37 52 8 10 3 0 0545 9 Bottom 11 12 implies find x such that P X x 0 1112 Look up p 1112 in the body of the table find z 1 22 So x z 52 8 1 22 10 3 52 8 12 566 40 234 years old On the calculator invNorm 0 1112 52 8 10 3 40 232 years old STAT 210 TEST 4 SOLUTIONS Version B 1 A C and D The Z distribution and all t distributions all have a bell shape a mean of zero and no unusual features The only difference between the Z and all t distributions is that they have different standard deviations 2 C A sampling distribution is the distribution of all values taken by a statistic in a large number of simple random samples of the same size from the same population 3 1 one The standard deviation of the standard normal Z distribution is one 4 0 zero The probability that a normal variable is exactly equal to any value is zero 5 P 40 X 57 P 57 49 3 Z 40 49 3 11 8 11 8 P 0 79 Z 0 65 P Z 0 65 P Z 0 79 0 7422 0 2148 0 5274 On the calculator normalcdf 40 57 49 3 11 8 0 5277 6 Top 1 46 implies find x such that P X x 0 0146 1 0 0146 0 9854 look up p 9854 in the body of the table find z 2 18 So x z 49 3 2 18 11 8 49 3 25 724 75 024 years old On the calculator invNorm 0 9854 49 3 11 8 75 033 years old 7 Bottom 18 14 implies find x such that P X x 0 1814 Look up p 1814 in the body of the table find z 0 91 So x z 49 3 0 91 11 8 49 3 10 738 38 562 years old On the calculator invNorm 0 1814 49 3 11 8 38 561 years old 8 P X 31 P Z 31 49 3 11 8 P Z 1 55 0 0606 On the calculator normalcdf 1E99 31 49 3 11 8 0 0605 9 P X 62 P Z 62 49 3 11 8 P Z 1 08 1 P Z 1 08 1 0 8599 0 1401 On the calculator normalcdf 62 1E99 49 3 11 8 0 1409 STAT 210 TEST 4 SOLUTIONS Version C 1 C A sampling distribution is the distribution of all values taken by a statistic in a large number of simple random samples of the same size from the same population 2 0 zero The mean of the standard normal Z distribution is zero 3 0 zero The probability that a normal variable is exactly equal to any value is zero 4 A B and D The Z distribution and all t distributions all have a bell shape a mean of zero and no unusual features The only difference between the Z and all t distributions is that they have different standard deviations 5 P X 27 P Z 27 47 8 12 6 P Z 1 65 1 P Z 1 65 1 0 0495 0 9505 On the calculator normalcdf 27 1E99 47 8 12 6 0 9506 6 P 52 X 64 P 64 47 8 Z 52 47 8 12 6 12 6 P 0 33 Z 1 29 P Z 1 29 P Z 0 33 0 9015 0 6293 0 2722 On the calculator normalcdf 52 64 47 8 12 6 0 2702 7 Top 2 62 implies find x such that P X x 0 0262 1 0 0262 0 9738 look up p 9738 in the body of the table find z 1 94 So x z 47 8 1 94 12 6 47 8 24 444 72 244 years old On the calculator invNorm 0 9738 47 8 12 6 72 242 years old 8 Bottom 13 35 implies find x such that P X x 0 1335 Look up p 1335 in the body of the table find z 1 11 So x z 47 8 1 11 12 6 47 8 13 986 33 814 years old On the calculator invNorm 0 1335 47 8 12 6 33 814 years old 9 P X 74 P Z 74 47 8 12 6 P Z 2 08 0 9812 On the calculator normalcdf 1E99 74 47 8 12 6 0 9812


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