Question

In this section, first identify the random variable(s) and its/their range (=possible values it could attain). Use 6 decimal places for best accuracy when dealing with numerical data.

Question 14 Take the following sample of student grades from a class: 70, 88, 91, 75, 79, 77, 70, 74, 81, 90

If these are assumed to represent the general pattern of the grades for the full class, use Chebychev’s inequality to give a lower bound on the probability that a given grade will be within 10 points of the average?

Answer 1

first of all we have to calculate mean and standard deviation for given data.

Standard Deviation, s: 7.8492745595444 Count, N: 10 Sum, Ex: 795 Mean, X: 79.5 Variance, s2: 61.611111111111 Steps N 1 S (xi – T)? N-1 i=1 s2 = E(xi - 7)2 N-1 (70 - 79.5)2 + ... + (90 - 79.5)2 10-1 554.5 9 = 61.611111111111 S = 161.611111111111 = 7.8492745595444 = =

nowt be within 10 points

P(ux - kox < X < Mx +ko y)21- k2 1- μχ- kσα Mx My+kog

k*s = 10

k= 10/7.8493 = 1.274

now lower bound is = 1-1/(1.274)²

0.3839

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