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.
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.