Answer:
a) the mean percentage of defective item produced is 2.52 %
b) the standard deviation of percentage of defective item produced is 1.01%
Step-by-step explanation:
Given that;
the percentage of defective items produced was 2%, 1.4%, 4%, 3%, 2.2%.
sample size n = 5
a) Calculate the mean for these data
mean percentage of defective item produced will be;
[tex]x^{bar}[/tex] = ∑x / n
[tex]x^{bar}[/tex] = ∑x / n = ( 2% + 1.4% + 4% + 3% + 2.2% ) / 5
[tex]x^{bar}[/tex] = 12.6 / 5
[tex]x^{bar}[/tex] = 2.52 %
Therefore, the mean percentage of defective item produced is 2.52 %
b) Calculate the standard deviation for these data
Formula for standard deviation is;
S = √( (∑(x-[tex]x^{bar}[/tex] )²) / (n-1) )
so we make a table;
x ( x - [tex]x^{bar}[/tex] )% ( x - [tex]x^{bar}[/tex] )²%
2% -0.52 0.2704
1.4% -1.12 1.2544
4% 1.48 2.1904
3% 0.48 0.2304
2.2%. -0.32 0.1024
summation 4.048
so (∑(x-[tex]x^{bar}[/tex] )² = 4.048%
so we substitute the value into our equation;
S = √( (∑(x-[tex]x^{bar}[/tex] )²) / (n-1) )
S = √( (4.048%) / (5-1) )
S = √( 4.048% / 4 )
S = √( 1.0121
S = 1.00598 % ≈ 1.01%
Therefore, the standard deviation of percentage of defective item produced is 1.01%
