Question

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

1. What is the random variable X described above? Write down the distribution of X using the standard notations.                                                                                                                                                                    

2. What are the mean and the variance of the dynamic viscosity of the given engine oil at 0 Celsius?

         

3. If a sample of the engine oil SAE 5W-40 at 0 Celsius is examined for dynamic viscosity, what is the probability that it would be greater than 755 millipascal-seconds?

4. 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? (You must define all the required parameters, and give the distribution in standard notations)

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

Answer 1

x-a © By Bits uniform distribution P( xcx)= b-a To find P(x > 755) = I - P(x <755) = 12 ( 755- 740 ) 760-7GO = 1 - 0.75 0.25 ../P(x>755)= 0.25

X is e.v.of dynamic valocity of engine oil oil SAE at 0° celsius. xn Uniform (a, b) a = 740 , b = 760 When anu(a,b) bex) = a sxsb b-d 6. H ㅗ IGO 3X2760 byro) = 470-74 o, ob (b To find mean atb Foot 760 mean = el = =750 2 2 mean = 750 (b-a) 2 Variance = (760-740)² u 12 12 - 20x20 12 - 93.93 [variance 33.39