In: Statistics and Probability
Answer:-
Given That:-
The piston rings are used to reject when a certain dimension is not within the specifications 1.5±d. It is known that this measurement is normally distributed with mean 1.50 mm and standard deviation 0.20 mm.
Given
mm
mm
X is random variable of dimension of piston ring.
We know for standard normal distribution 90% area lies between -1.645 to + 1.645
Therefore 90% area lies between 1.645 standard deviation
Therefore d = 1.645 ()
= 0.329
(4). Find the value d such that the specifications cover 90% of the measurements.?
Value of d = 0.329
Lower specification limit = 1.5 - 0.329
= 1.171 mm
Upper specification limit = 1.5 + 0.329
= 1.829 mm
(5) What is the probability that the measurement of a selected piston ring will be more than 3 mm?
= P(Z > 7.5)
= 1 - P ( Z < 7.5)
= 1 - 1
= 0
Therefore Around 0% ring have more than 3 mm dimension.
Plz like it.....,