a company manufactures batteries in batches of 18 and there is a 3% defect rate. Find the standard deviation for a number of defects per batch?
To find the standard deviation for the number of defects per batch, we can use the formula for the standard deviation of a binomial distribution.
Step 1: Determine the probability of a defect in each battery.
The defect rate is given as 3%, which is equivalent to 0.03. So, the probability of a defect in each battery is 0.03.
Step 2: Determine the probability of no defect in each battery.
The complement of the probability of a defect is the probability of no defect. Therefore, the probability of no defect in each battery is 1 - 0.03 = 0.97.
Step 3: Calculate the mean number of defects per batch.
Since the defect rate is 3% and there are 18 batteries in each batch, the mean number of defects per batch can be calculated by multiplying the number of batteries by the defect rate: 18 x 0.03 = 0.54.
Step 4: Calculate the standard deviation using the formula.
The formula for the standard deviation of a binomial distribution is √(n * p * (1 - p)), where n is the number of trials (in this case, 18) and p is the probability of success (in this case, 0.03).
Standard deviation = √(18 * 0.03 * 0.97) = √(0.4914) ≈ 0.7005.
Therefore, the standard deviation for the number of defects per batch is approximately 0.7005.
To find the standard deviation for the number of defects per batch, we first need to calculate the variance. The variance measures the spread of the data, and the standard deviation is the square root of the variance.
In this case, the company manufactures batteries in batches of 18, and there is a 3% defect rate. We can calculate the variance for the number of defects per batch using the following formula:
Variance = (Number of Trials) * (Probability of Success) * (Probability of Failure)
Here, the number of trials is the number of batteries in each batch (18), the probability of success is the defect rate (3% or 0.03), and the probability of failure is 1 minus the defect rate (1 - 0.03 = 0.97).
Variance = 18 * 0.03 * 0.97 = 0.5244
Now, to find the standard deviation, we take the square root of the variance:
Standard Deviation = √(Variance) = √(0.5244) ≈ 0.7244
Therefore, the standard deviation for the number of defects per batch is approximately 0.7244.
A company manufactures batteries in batches of 15 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch
standard deviation = √npq = √(18 * .03 * .97) = ?
Note: q = 1 - p
I'll let you finish the calculation.