Question

In: Statistics and Probability

(4). Find the value d such that the specifications cover 90% of the measurements. (5). What...

(4). Find the value d such that the specifications cover 90% of the measurements.

(5). What is the probability that the measurement of a selected piston ring will be more than 3 mm?

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.

(4). Find the value d such that the specifications cover 90% of the measurements.?

(. What is the probability that the measurement of a selected piston ring will be more than 3 mm?

Expert Solution

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

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.....,

orchestra answered 2 years ago

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