The standard deviation for the number of defects per batch is 0.5
In binomial distribution, standard deviation is given as:
[tex]\sigma=\sqrt{np(1-p)}[/tex]
Where "n" is the number of observations
"p" is probability of getting success
We are given that ,
Total batches of televisions : n = 25
The probability of defects : p = 1% = 0.01
Here success is getting defective batch
Then, the standard deviation for the number of defects per batch will be:
Plugging in values in formula, we get
[tex]\sigma=\sqrt{(25)(0.01)(1-0.01)}\\\\=\sqrt{(25)(0.01)(0.99)}\\\\=\sqrt{0.2475}\\\\=0.497493718553\approx0.5[/tex]
Therefore, the standard deviation for the number of defects per batch = 0.5
