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.
The formula for the standard deviation of a binomial distribution is:
σ = √(n * p * (1 - p))
Where:
σ = standard deviation
n = number of trials (or in this case, number of televisions in a batch) = 25
p = probability of success (or in this case, the defect rate) = 1% or 0.01
Plugging in the values, we get:
σ = √(25 * 0.01 * (1 - 0.01))
Calculating this, we have:
σ = √(25 * 0.01 * 0.99)
σ = √0.2475
σ ≈ 0.497
Therefore, the standard deviation for the number of defects per batch is approximately 0.497.
A company manufactures televisions in batches of 25 and there is a one percent rate of defects. Find the standard deviation for the number of defects per batch.
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