A company manufacturers batteries of 18 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.
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"A company manufacturers batteries IN BATCHES of 18 and there is a 3% rate of defects." ? Your question makes no sense as you have written it
Yes, I meant to write, "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.
Yes my question is right that what my teacher has on my homework sheet
To find the standard deviation for the number of defects per batch, we need to use the binomial distribution formula. The binomial distribution models the probability of a certain number of successes (defects in this case) in a fixed number of trials (batches). In this case, each battery in a batch can either be defective (failure) with a probability of 3% or non-defective (success) with a probability of 97%.
The standard deviation of a binomial distribution is calculated using the formula:
Standard Deviation = sqrt(n * p * (1 - p))
where:
- n is the number of trials (batteries in a batch)
- p is the probability of success (defect rate)
In this case, n = 18 (since each batch contains 18 batteries) and p = 0.03 (3% defect rate).
Substituting these values into the formula, we get:
Standard Deviation = sqrt(18 * 0.03 * (1 - 0.03))
Calculating this expression, we get:
Standard Deviation ≈ 1.326
So, the standard deviation for the number of defects per batch is approximately 1.326.