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13. + 1/2 points Previous Answers TanFin 12 8.3.041.CMI. A probability distribution has a mean of 48 and a standard deviation of 2. Use Chebychev's inequality to find a bound on the probability that an outcome of the experiment lies between the following. (a) 44 and 52 at least 84 * % (b) 38 and 58 at least 96 % Need Help? Read It Watch It 14. + 0/2 points Previous Answers TanFin 12 8.3.042.CMI. A probability distribution has a mean of 30 and a standard deviation of 3. Use Chebychev's inequality to find a bound on the probability that an outcome of the experiment lies between the following. (a) 25 and 35 at least 34 x % (b) 20 and 40 at least 84 x % Need Help? Read It Watch It Submit Answer Practice Another Version

Answer 1

Given that, u = 48,0 = 2 k= X-_ 44 – 48 = -2 o 2 k-X-u_52-48 o 2 - From chebyshev's inequality, p21- > 1-0.25 > 0.75 Therefore, 75% of outcome of the experiment lies between 44 and 52. Given that, u = 48,0 = 2 E-X-4_38-48 O2=-5 k-X- \ _ 58-48 o 2 From chebyshev's inequality,

p21- 21-5 21-0.04 > 0.96 Therefore, 96% of outcome of the experiment lies between 38 and 58. Given that, u = 30,0 = 3 k=*=4-25-30 = -1.6667 o 3 k=x-u - 35-30 o 3 =1.6667 From chebyshev's inequality, p21- 1-2 1.66672 >1-0.36 > 0.64

Therefore, 64% of outcome of the experiment lies between 25 and 35. b) Given that, u = 30,0 = 3 k-X-4_20-30 =-3.3333 o 3 k=X-4_40-30 -=3.3333 From chebyshev's inequality, p21 21- 21-3.3333 1 >1-0.09 > 0.91 Therefore, 91% of outcome of the experiment lies between 20 and 40.