Question

The dynamic viscosity of the engine oil SAE 5W-40 at 0 Celsius follows a Uniform Distribution from 740 to 760 millipascal-seconds.

1)Take 16 samples of engine oil SAE 5W-40 and examine the dynamic viscosities at 0 Celsius: what should be the distribution of the mean dynamic viscosity?

2)For the 16 samples taken in step (above), what should be the probability that the sample mean dynamic viscosity is greater than 755 millipascal-seconds?

Answer 1

a) We are given the underlying distribution here as:

$X \sim U(a = 740, b = 760)$

The mean and standard deviation here are computed as:

$E(X) = \frac{a + b}{2} =\frac{740 + 760}{2} = 750$

$SD(X) = \frac{(b - a)}{\sqrt{12}} = \frac{760 - 740}{\sqrt{12}} = 5.7735$

Therefore the distribution of the sample mean here is computed as:

X N N[// = 750, 7 T = 5.7735, V16

X Nu = 750,0 = 1.4434)

this is the required distribution of mean dynamic viscosity here.

b) The probability here is computed as:

$P(\bar X > 755)$

Converting it to a standard normal variable, we have here:

$P(Z > \frac{755 - 750}{1.4434})$

Getting it from the standard normal tables, we have here:

Therefore 0.0003 is the required probability here.