Please solve the following and show work please

1. (10 points) Use the Gaussian Elimination or Matrix Inversion (no points for any other method) to solve: 1x + 2y + 32 = 14 2x + ly + 3z = 13 2x + 3y + 12 = 11 2. (10 points) The relative frequency/probability distribution of number of TVs sold in a day at a store is as follows: Number of TV sold 0 1 2 3 4 Relative Frequency (probability) 0.1 0.5 0.25 0.1 0.05 Compute the mean and standard deviation of this distribution. 3. Human IQ scores are approximately normally distributed with mean 100 and standard deviation 15. Determine: (a) (5 points) the probability that a person will have IQ of less than 90, (b) (5 points) the minimum IQ score for the top 5% of the population. 4. (15 points) The Initial diagnosis of a patient's illness was tentially flu (F), cold (C), or hay fev (H), with probabilities 0.1,0.2, and 0.7 respectively. A lab test was then given to the patient. Past tests on similar patients show the following conditional probabilities on the test result being positive (+), neutral (0), or negative (-) given that the patient is eventually determined to have F, C, or H: Pf+IF) = 0.7 POLF) = 0.2 PC-1F) = 0.1 Pl+C) = 0.1 P( OC) = 0.8 PC-IC) = 0.1 PL+1H) = 0.1 PIOTH) = 0.3 PC-TH) = 0.6 Use Bayes Theorem to estimate the respective 9 conditional probabilities of F, C, and H given that a +, 0, or- test result has been observed