Question

Suppose we are given a probability distribution that has a mean if 12 and a standard deviation of 0.2. Use the Chebyshev inequality to find a lower bound estimate of the following probabilities: (a) The probability that the outcome will lie between 10 and 14 (b) The probability that the outcome lies between 10.5 to 13.5
Problem #1(a):	Round your answer to 4 decimals.
Problem #1(b):	Round your answer to 4 decimals.

Answer 1

Given: Mean M=12 Standard deviation &=0.2. (a) Chebeshow's inequality states that p[Yx-Ecm)] <K)x1 - verb ie P [ix-jekk] >, is F 1 E 1 Now, P(10<x<14) = P110-12 < x-u<14-12) = P(-2<x-4<2) = Pl 1x-<2). New by chebyshen's Inequality, P(IX-M1<2)>, i-o2 = -0.04 =1-0001 = P(1x-pel<2) >0.99 fie Pliocx<14) is 70.99 (b) P110.5< x < 135)= P(10.5-18 < x-pe</3.5-12) = PE 1.5 < x-pe<105) =P(1x-p/ <105) By chebysheus Inequality 1 1 1 1 O P (lx-M1 <105) > T-110a - 0.04 2. as - 1-0.01778 =0.8222 : PI 10:5 < X <13-5) >, 0.8222 Scanned with CamScanner