PLEASE HELP me solve the following problem:
A computer diskette manufacturer is concerned that some diskettes have bad sectors that would cause a diskette to hold less information that it was intended to hold. In the past, only 5% of these diskettes have had bad sectors. If the company wishes to use 99.7% control limits based on samples of size 500, what would these limits be. LCL = _____ and UCL = _____??? Thanks.
Lower limits = mean - 3(sd/√n)
Upper limits = mean + 3(sd/√n)
mean = np
sd = √npq
n = 500
p = .05
q = 1 - p
Calculate the lower and upper limits using the mean, standard devation, and sample size.
I hope this helps.
THANK YOU, MathGuru, for your help!
To solve this problem, we can use the concept of binomial distribution and control charts.
Given that in the past, only 5% of the diskettes have had bad sectors, we can assume that this proportion remains the same for the future as well.
To set up the control limits for the proportion of bad sectors, we need to calculate the upper control limit (UCL) and lower control limit (LCL) using the 99.7% control limits.
Here are the steps to calculate the control limits:
Step 1: Calculate the standard deviation (sigma):
The standard deviation (sigma) can be calculated using the formula:
sigma = sqrt((p*(1-p))/n)
Where:
- p is the proportion of bad sectors (0.05 in this case)
- n is the sample size (500 in this case)
Plugging in the values:
sigma = sqrt((0.05*(1-0.05))/500)
Step 2: Calculate the Z value:
We need to calculate the Z value for the desired confidence level. In this case, the desired confidence level is 99.7%, which corresponds to a Z value of 3.
Z = 3
Step 3: Calculate the control limits:
The control limits are calculated using the formula:
LCL = p - Z*sigma
UCL = p + Z*sigma
Plugging in the values:
LCL = 0.05 - 3*sigma
UCL = 0.05 + 3*sigma
Now, to get the final answer, we need to calculate the values of LCL and UCL by substituting the respective values in the formulas.
I will now calculate the LCL and UCL for you.