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Review course lecture material, and Section 6.8.3 within the textbook. Complete and post the following problems. 1. We have a population that is normally distributed. A sample of 10 gives an average of 4.00 and a standard deviation of 1.873. What is the probability of pulling a single sample between 3 and 5? Use the posted Table for the Student t distribution. The pdf file is located directly beneath the assignment document. Use that table to solve these two problems. Use linear interpolation to solve (basic algebra) these two problems. 2. From the above problem; what is the probability of pulling a single sample less than 1.6?Table A-2 The t distribution The entry in row k (degrees of freedom) under column heading p (probability) is the value t* for which P(O<1)1*) = p. p 0.05 0.1 0.2 0.25 0.3 0.4 0.45 0.475 0.49 0.495 k 1 158 .325 .727 1.000 1.376 3.08 6.31 12.71 31.82 63.66 2 .142 .289 .617 .816 1.061 1.89 2.92 4.30 6.96 9.92 3 .137 .277 .584 .765 .978 1.64 2.35 3.18 4.54 5.84 4 .134 .271 .569 .741 .941 1.53 2.13 2.78 3.75 4.60 5 .132 .267 .559 .727 .920 1.48 2.02 2.57 3.36 4.03 6 .131 .265 .553 .718 .906 1.44 1.94 2.45 3.14 3.71 7 .130 .263 .549 .711 .896 1.42 1.90 2.36 3.00 3.50 8 .130 .262 .546 .706 .889 1.40 1.86 2.31 2.90 3.36 9 .129 .261 .543 .703 .883 1.38 1.83 2.26 2.82 3.25 10 .129 .260 .542 .700 .879 1.37 1.81 2.23 2.76 3.17 11 .129 .260 .540 .697 .876 1.36 1.80 2.20 2.72 3.11 12 .128 .259 .539 .695 .873 1.36 1.78 2.18 2.68 3.06 13 .128 .259 .538 .694 .870 1.35 1.77 2.16 2.65 3.01 14 .128 .258 .537 .692 .868 1.34 1.76 2.14 2.62 2.98 15 .128 .258 .536 .691 .866 1.34 1.75 2.13 2.60 2.95 16 .128 .258 .535 .690 .865 1.34 1.75 2.12 2.58 2.92 17 .128 .257 .534 .689 .863 1.33 1.74 2.11 2.57 2.90 18 .127 .257 .534 .688 .862 1.33 1.73 2.10 2.55 2.88 19 .127 .257 .533 .688 .861 1.33 1.73 2.09 2.54 2.86 20 .127 .257 .533 .687 .860 1.32 1.72 2.09 2.53 2.84 21 .127 .257 .532 .686 .859 1.32 1.72 2.08 2.52 2.83 22 .127 .256 .532 .686 .858 1.32 1.72 2.07 2.51 2.82 23 .127 .256 .532 .685 .858 1.32 1.71 2.07 2.50 2.81 24 .127 .256 .531 .685 .857 1.32 1.71 2.06 2.49 2.80 25 .127 .256 .531 .684 .856 1.32 1.71 2.06 2.48 2.79 26 .127 .256 .531 .684 .856 1.32 1.71 2.06 2.48 2.78 27 .127 .256 .531 .684 .855 1.31 1.70 2.05 2.47 2.77 28 .127 .256 .530 .683 .855 1.31 1.70 2.05 2.47 2.76 29 .127 .256 .530 .683 .854 1.31 1.70 2.04 2.46 2.76 30 .127 .256 .530 .683 .854 1.31 1.70 2.04 2.46 2.75 40 .126 .255 .529 .681 .851 1.30 1.68 2.02 2.42 2.70 60 .126 .254 .527 .679 .848 1.30 1.67 2.00 2.39 2.66 120 .126 .254 .526 .677 .845 1.29 1.66 1.98 2.36 2.62 8 .126 .253 524 .674 .842 1.28 1.645 1.96 2.33 2.58 Source: R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research, published by Longman Group Ltd., London (previously published by Oliver and Boyd, Edinburgh), and by permission of the authors and publishers.

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