Question

A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug airtight. An air needle was inserted into the plug, which was then placed underwater. Next, the pressure was increased until leakage was observed. The magnitude of this pressure in psi was recorded for 10 trials: 3.1 3.5 3.3 3.7 4.5 4.2 2.8 3.9 3.5 3.3 Find the sample mean and sample standard deviation for these 10 measurements.

Answer 1

`\bar X = (3.1+3.5+3.3+3.7+4.5+4.2+2.8+3.9+3.5+3.3)/(10)= 3.58`

And the sample deviation with the following formula:

`s= \sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

And replacing we got:

`s = 0.512`

And then the answer is :

`\bar X= 3.58, \sigma = 0.512`

Explanation:

For this case we have the following data given:

3.1 3.5 3.3 3.7 4.5 4.2 2.8 3.9 3.5 3.3

The sample mean can be calculated with this formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And replacing we got:

`\bar X = (3.1+3.5+3.3+3.7+4.5+4.2+2.8+3.9+3.5+3.3)/(10)= 3.58`

And the sample deviation with the following formula:

`s= \sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

And replacing we got:

`s = 0.512`

And then the answer is :

`\bar X= 3.58, \sigma = 0.512`