A company manufactures calulatoirs in batches of 64 and ther is a 5% 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 follow these steps:
Step 1: Calculate the expected number of defects per batch.
The defect rate is given as 5%, which means there is a 5% chance of a calculator being defective. This can also be expressed as a probability of 0.05.
Expected number of defects per batch = Probability of defect * Number of calculators per batch
Expected number of defects per batch = 0.05 * 64
Expected number of defects per batch = 3.2
So, on average, we expect 3.2 defects per batch.
Step 2: Calculate the variance of the number of defects per batch.
Variance = Probability of defect * (Number of calculators per batch - Expected number of defects per batch)^2
Variance = 0.05 * (64 - 3.2)^2
Variance = 0.05 * 60.8^2
Variance = 0.05 * 3696.64
Variance = 184.832
So, the variance of the number of defects per batch is 184.832.
Step 3: Calculate the standard deviation.
Standard Deviation = Square root of Variance
Standard Deviation = √184.832
Standard Deviation ≈ 13.602
Therefore, the standard deviation for the number of defects per batch is approximately 13.602.