re1 to compute and Problem 31 Use test score distribution f

re#1 to compute and . Problem 3-1: Use test score distribution from Lecture# 1 to compute

Solution

1) Using the provided formulae,

<s²>=3/28*60²+5/28*70²+10/28*80²+6/28*90²+4/28*100²=6710.71

Also as given, <s>=81.1, thus <s>²=81.1²=6577.21

2) Del s= s-<s>

Thus <(Del s)²>=3/28*(60-81.1)²+5/28*(70-81.1)²+10/28*(80-81.1)²+6/28*(90-81.1)²+4/28*(100-81.1)²=133.6

sigma= sqrt(<(Del s)²>)=11.6

3)sigma=sqrt(<s²>-<s>²)=sqrt(6710.71-6577.21)=11.6

thus they are both equal.