Question

A company makes parts for a medical machine. The lengths of the parts must be within certain limits or they will be rejected.
A large number of parts were measured and the mean and standard deviation were calculated as 3.1 m and 0.005 m respectively.
Assuming this data is normally distributed and 99.7% of the parts were accepted, what are the limits?

Answer 1

The required limit of 99.7%, normally distributed, parts that is accepted is (3.085, 3115).

Given that,

In the question sample mean ( M ) is 3.1 m, the standard deviation ( σ ) is 0.005 m, and the percentage of parts accepted is 99.7%.

What is Statistic?

Statistic is defined as the mathematical analysis dealing with relations between comprehensive data.

Applying Empirical Rule,
Here, 99.7% of data followed a normal distribution,
Distribution along the mean or limits be;
Distribution or limit = M ± 3σ

Limit = 3.1 ± (3 . 0.005)

Limit = 3.1 ± 0.015
Limit = {(3.1 - 0.015), (3 + 0.015)}

Limit = {3.085, 3.115}

Thus, the required limit of 99.7%, normally distributed, parts that is accepted is (3.085, 3115).

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