Can someone provide me with some assistance in answering this question..

A company manufacturers batteries in BATCHES of 18 and there is a 3% rate of defect. Find the standard deviation for the number of defects per batch.

The probability of a defect is p = 0.03

The mean number of defects in a batch of N = 18 is m = p N = 0.03 x 18 = 0.54

The standard deviation of the number of defects in a batch of 18 is
sigma = sqrt [N p (1-p)] = 0.72, which actually exceeds the mean value in this case.

Can you explain how you got the standard deviation of the number of defects in a batch of 18 is sigma=sqrt[N p (1-p)]=0.72. IN OTHER WORDS HOW DID YOU GET 0.72

To calculate the standard deviation for the number of defects per batch, you can use the formula:

standard deviation (σ) = √[N * p * (1 - p)]

where N is the number of batteries in a batch (which is 18 in this case) and p is the probability of a defect (which is 0.03 or 3%).

First, let's calculate the mean number of defects:

mean number of defects (m) = p * N = 0.03 * 18 = 0.54

Now, substitute the values into the standard deviation formula:

σ = √[18 * 0.03 * (1 - 0.03)]
= √[0.54 * 0.97]
≈ √0.5248
≈ 0.72

So, the standard deviation for the number of defects per batch is approximately 0.72.

It's interesting to note that the standard deviation in this case exceeds the mean value, indicating that there may be a significant amount of variation in the number of defects per batch.