Statistics

Q2. (3) (b) (C) (Write down the measurement unit when applicable and correct your answers to 4 decimal places.) According to the guideline from Dental Association, a dentist can use up to a maximum of 5 times of nitrous oxide (\"laughing gas\") in a single treatment. Let X be the number of times of nitrous oxide being used by a dentist in a single treatment. The probability distribution of X is as follows: _-i)2--0.14-____ 0.27 0.16 0.05 P(X= x) 0.36 Find the expectation of X. (2 marks) Find the variance of X. (2 marks) A researcher is reviewing reports of 5 independent treatments conducted by this dentist. What is the probability that among the 5 treatments, exactly 2 of them have used nitrous oxide for O or 1 time? (6 marks) (Total: 10 marks) Applied Statistics The entries in Table II are values for which the area to their right under the The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given distribution with given degrees of freedom (the gray area in the figure) is equal by the area of the gray region under the curve in the figure. to a TABLE II TABLE I NORMAL-CURVE AREAS d.f. to.050 to.025 to.010 to.005 d.f. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 12.706 2.920 4.30 6.965 9.92 0.0 0.0160 0.0239 2.353 3.18 4.541 5.841 0.0398 0.0438 0.0557 4.604 0.2 0.0910 0.0948 .132 2.77 3.747 0.3 0.1179 0.1255 0. 1406 2.015 2.571 3.365 4.032 0.4 0.1554 0.1628 0.1664 0.1700 3.707 0.1915 0.2054 0.2123 1.943 2.44 3.143 0.5 0.1985 0.2088 1.895 2.36 2.99 3.49 0.6 0.2257 0.2291 1.860 2.896 3.355 0.7 0 8 0.2967 0.2995 0.3023 1.833 2.262 2.821 3.250 0.9 0.3159 0.3238 0.3264 0.3289 1.812 2.22 2.764 1.0 0.3413 0.3461 0.3485 0.3508 0.3531 0.3554 1.796 2.20 0.3643 0.3729 0.3749 0.3770 1.2 0.3849 0.3907 0.3925 0.3944 0.3962 0.3980 .782 2.17 2.681 .055 0.4066 0.4099 0.4115 0.4131 1.771 2.16 3.012 1.3 0.4032 1.4 0.4192 0.4207 0.4236 0.4251 0.4265 0.4306 1.761 2.14 2.624 15 0.4332 0.4357 0.4382 0.4406 1.753 2.13 2.602 2.947 15 0.4452 0.4495 0.4515 0.4535 .746 2.583 2.921 1.7 0.4554 0.4573 0.4582 0.4591 0.4599 1.8 0.4641 0.4648 0.4656 0.4678 0.4685 1.740 2.110 2.567 2.898 17 1.9 0.4713 0.4725 0.4732 0.4738 0.4744 0.4750 0.4756 1.734 2.10 2.552 18 2.0 0.4772 0.4783 0.4793 0.4798 0.4803 0.4812 1.729 2.09 2.539 19 2.1 0.4821 0.4830 0.4838 0.4850 0.4854 .725 2.08 2.845 20 0.4864 0.4875 0.4878 0.488 0.4893 0.4896 0.4898 0.4901 0.491 0.4913 1.721 2.518 2.831 21 0.4918 0.4920 0.4922 0.4927 0.4929 0.4931 0.4934 1.717 2.508 0.4938 0.4941 0.4943 0.4945 0.4948 1.714 2.06 2.500 23 2.6 0.4956 0.4957 0.4959 0.4961 0.4963 1.711 2.06 2.492 2.797 2.7 0.4965 0.4967 0.4968 0.4969 0.4970 0.4971 0.4973 0.4980 1.708 2.060 2.485 2.787 25 2.8 0.4974 0.4975 0.4976 0.4978 29 0.4982 0.4983 0.4984 0.4985 1.706 2.05 2.479 2.779 3.0 0.4987 0.4988 0.4988 .4990 0.4990 1.703 2.05 2.473 1.701 2.048 2.467 2.763 1.699 2.04 2.462 2.756 1.645 1.960 2.326