A company manufactures calculators in batches of 64 and there is a 5% rate of defects. What is the standard deviation for the number of defects per batch?

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To find the standard deviation for the number of defects per batch, we need to use the formula for the standard deviation of a binomial distribution. In this case, the number of defects follows a binomial distribution with parameters n (batch size) and p (defect rate).

The formula for the standard deviation of a binomial distribution is:

σ = √(n * p * (1 - p))

In this case, the batch size is 64 and the defect rate is 5% or 0.05. Let's plug these values into the formula:

σ = √(64 * 0.05 * (1 - 0.05))

σ = √(64 * 0.05 * 0.95)

σ = √(3.84)

σ = 1.96

Therefore, the standard deviation for the number of defects per batch is approximately 1.96.