Answer:
The standard deviation for the number of defects per batch is 0.87.
Step-by-step explanation:
Let X denote the number of defective batteries per batch.
A company manufactures batteries in batches of n = 26.
It is provided that the rate of defects is, p = 0.03.
Each battery is defective independently of the others.
The random variable X follows a binomial distribution.
The standard deviation of a binomial distribution is:
[tex]\sigma=\sqrt{np(1-p)}[/tex]
Compute the standard deviation for the number of defects per batch as follows:
[tex]\sigma=\sqrt{np(1-p)}[/tex]
[tex]=\sqrt{26\times 0.03\times (1-0.03)}\\\\=0.86982757\\\\\approx 0.87[/tex]
Thus, the standard deviation for the number of defects per batch is 0.87.
