\fApplications of the Normal Distribution 1. On the assumptions that IQ's are normally distributed in the population with a mean of 100 and a standard deviation of 20. (15 points) a. What is the probability of scoring between 90 and 120? b. What percentage of the cases cannot score more than 110? c. What is the proportion of scoring above 135? 2. In an aptitude test given to a group of 200 applicants, the average score was 75 and the standard deviation was 5. The scores are approximately normally distributed. (10 points) a. About how many applicants got scores above 66? b. About how many applicants got scores between 70 and 80?l. Determine the following areas under the standard normal curve. (15 points} 1. Area to the right of: = 2.32 2. Area to the n'ghtofz = 1.53 3. Area to the left of: = 43.94 4. Area between 2 = 1.15 and z = 2.23 5. Area between 2 = 1.t]9 and z = 2.2? II. Given a normal distribution with f = 180 and e = 20. nd: [20 points} 1. The area above 230 2. The area below 215 3. The area above we 4. The area between 160 and 200 5. The area between 185 and 225 State whether each hypothesis is null or alternative hypothesis. 1. The proportion of patients with lung disease is higher among smokers than among non-smokers. 2. There is no difference between drug X and drug Y in relieving muscle pains. 3. Children using brand A toothpaste have fewer cavities than those using brand B toothpaste. 4. There is a difference in the durability oftwo different brands of watches. 5. A wholesome advertisement will not lead to increased sales for the product. State whether each alternative hypothesis is directional or nondirectional hypothesis. 1. Improved working conditions in a plant will lead to greater productivity. 2. The average nicotine content per stick of cigarette is not 2.1 mg. 3. The average recovery time of a patient taking a particular medication is less than one month. 4. The GE 3 grades of BSEd 1 students is not the same as the GE 3 grades of BEEd 1 students. 5. There is a signicant difference between the performance of the faculty from the different colleges. State whether each alternative hypothesis uses a one-tailed or two-tailed test. 1. Improved working conditions in a plant will lead to greater productivity. 2. The average nicotine content per stick of cigarette is not 2.1 mg. 3. The average recovery time of a patient taking a particular meditation is less than one month. 4. The GE 3 grades of BSEd 1 students is not the same as the GE 3 grades of BEEd 1 students. 5. There is a signicant difference between the performance of the faculty from the different colleges. Test the hypothesis of the following problems. 1. An instructor gives his class an achievement test which as he knows from years of experience, yields a mean of 80. His present class of 40 obtains a mean of 85 and a standard deviation of 8. Can he claim that his class is a superior class? Use 1% level of signicance. The mean content of 25 bottles of brand Z mangojuice is 355 mL with a standard deviation of 9 mL. Is this in line with the manufacturer's claim that the bottles contain. on the average. 360 mL? Table 9.4 Students t - Distribution Table Level of Significance for a One-Tailed Test Degrees of .25 .20 .15 .10 .05 .025 .01 005 .0005 Freedom (n-1) Level of Significance for a Two-Tailed Test 50 40 .30 .20 .10 .05 .02 .001 1.000 1.376 1.963 3.078 6.314 12.706 31.821 63.657 636.619 .816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 31.598 LAWN - .765 978 1.250 1.638 2.353 3.182 4.541 5.841 12.924 .741 .941 1.190 1.533 2.132 2.776 3.747 4.604 8.610 .727 .920 1.156 1.476 2.015 2.571 3.365 4.032 6.869 .718 .906 1.134 1.440 1.943 2.447 3.143 3.707 5.959 711 .896 1.119 1.415 1.895 2.365 2.998 3.499 5.408 .706 .889 1.108 1.397 1.860 2.306 2.896 3.355 5.041 .703 .883 1.100 1.383 1.833 2.262 2.821 3.250 4.781 .700 .879 1.093 1.372 1.812 2.228 2.764 3.169 4.587 697 876 1.088 1.363 1.796 2.201 2.718 3.106 4.437 .695 .873 1.083 1.356 1.782 2.179 2.681 3.055 4.318 .694 870 1.079 1.350 1.771 2.160 2.650 3.012 4.221 .692 .868 1.076 1.345 1.761 2.145 2.624 2.977 4.140 .691 .866 1.074 1.341 1.753 2.131 2.602 2.947 4.073 .690 865 1.071 1.337 1.746 2.120 2.583 2.921 4.015 .689 .863 1.069 1.333 1.740 2.110 2.567 2.898 3.965 .688 .862 1.067 1.330 1.734 2.101 2.552 2.878 3.922 .688 .861 1.066 1.328 1.729 2.093 2.539 2.861 3.883 .687 .860 1.064 1.325 1.725 2.086 2.528 2.845 3.850 .686 .859 1.063 1.323 1.721 2.080 2.518 2.831 3.819 686 858 1.061 1.321 1.717 2.074 2.508 2.819 3.792 585 .858 1.060 1.319 1.714 2.069 2.500 2.807 3.767 585 857 1.059 1.318 1.711 2.064 2.492 2.797 3.745 684 856 1.058 1.316 1.708 2.060 2.485 2.787 3.725 .684 856 1.058 1.315 1.706 2.056 2.479 2.779 3.70 .684 855 1.057 1.314 1.703 2.052 2.473 2.771 3.690 . 683 855 1.056 1.313 1.701 2.048 2.467 2.763 3.674 .683 854 1.055 1.311 1.699 2.045 2.462 2.756 3.659 .683 .854 1.055 1.310 1.697 2.042 2.457 2.750 3.646 .681 .851 1.050 1.303 1.684 2.021 2.423 2.704 3.551 .679 .848 1.046 1.296 1.671 2.000 2.390 2.660 3.460 8 8 8 8 .677 845 1.041 1.289 1.658 1.980 2.358 2.617 3.373 .674 842 1.036 1.282 1.645 1.960 2.326 2.576 3.291