To monitor the number of blemishes on a polished surface,a company randomly selects 10 units of output from its process and counts the number of blemishes on each unit.The sample results are shown below: Given the sample information above,the standard deviation of the number of defects for this process would be
A)16.
B)10.
C)4.
D)0.

Question

To monitor the number of blemishes on a polished surface,a company randomly selects 10 units of output from its process and counts the number of blemishes on each unit.The sample results are shown below:  Given the sample information above,the standard deviation of the number of defects for this process would be
A)16. 
B)10. 
C)4. 
D)0.

Quizplus · Accepted Answer

To find the standard deviation, we need to calculate the variance first. The formula for variance is:

s^2 = Σ(x-μ)^2/n

Where s^2 is the variance, Σ is the sum of, x is the number of blemishes on each unit, μ is the mean of the number of blemishes, and n is the sample size (10 in this case).

First, we need to find the mean (μ) of the number of blemishes:

μ = Σx/n = (2 + 6 + 0 + 1 + 4 + 3 + 5 + 0 + 7 + 2)/10 = 3

Next, we can plug in the values to calculate the variance:

s^2 = [(2-3)^2 + (6-3)^2 + (0-3)^2 + (1-3)^2 + (4-3)^2 + (3-3)^2 + (5-3)^2 + (0-3)^2 + (7-3)^2 + (2-3)^2]/10
s^2 = 56/10
s^2 = 5.6

Finally, we take the square root of the variance to get the standard deviation:

s = √5.6 ≈ 2.37

Therefore, the best choice is C, with a standard deviation of about 2.37.

To Monitor the Number of Blemishes on a Polished Surface,a