Question

Apollo medical supplies produces hypodermic needles. For a particular type of needle, the average length should be 70 mm, and it is estimated that the standard deviation of the system is 1.25 mm. Apollo conducts quality control by taking a sample of 16 random needles every hour. Below is the mean of 5 hours’ worth of samples. Sample Length (mm) 1 69 2 72 3 71 4 70 5 68 What would be the upper control level with a 99.7% level of confidence?

Answer 1

Answer:

70.94 mm is the upper control level with a 99.7% level of confidence.

Step-by-step explanation:

We are given the following data:

69, 72, 71, 70, 68

Population mean = 70 mm

Population standard deviation = 1.25 mm

We have to find the upper control level with a 99.7% level of confidence.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{350}{5} = 70$

99.7% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.003} = \pm 2.98$

$70 \pm 2.98(\frac{1.25}{\sqrt{16}} ) = 70 \pm 0.93125 = (69.06875,70.93125) \approx (69.07,70.94)$

Thus, 70.94 mm is the upper control level with a 99.7% level of confidence.