A company manufactures televisions in batches of 25 and there is a 1% 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 apply the formula:
Standard Deviation = Square Root of (Variance)
We first need to calculate the variance. The variance of a binomial distribution can be found using the formula:
Variance = n * p * (1 - p)
Where:
n = number of trials or observations (batch size)
p = probability of success (rate of defects)
In this case, the batch size is 25 (n = 25) and the rate of defects is 1% or 0.01 (p = 0.01).
Variance = 25 * 0.01 * (1 - 0.01)
Variance = 25 * 0.01 * 0.99
Variance = 0.2475
Now, we can calculate the standard deviation using the formula:
Standard Deviation = Square Root of (Variance)
Standard Deviation = Square Root of (0.2475)
Standard Deviation ≈ 0.4975
Therefore, the standard deviation for the number of defects per batch is approximately 0.4975.