Question

2. A company makes parts for a 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

Assuming the given data is normally distributed and 99.7% of the parts were accepted, the limits will be; Between 3.085 m and 3.115 m

We are given;

Sample mean; x' = 3.1 m

Standard deviation; σ = 0.005 m

Percentage of parts accepted = 99.7%

According to the Empirical Rule, it states that 99.7% of data observed following a normal distribution will lie within 3 standard deviations of the mean.

Thus, the limits will be;

Interval = x' ± 3σ

Interval limit = 3.1 ± (3 × 0.005)

Interval limit = 3.1 ± 0.015

Interval limit = (3.1 - 0.015), (3 + 0.015)

Interval limit = (3.085, 3.115)

Read more about the empirical rule at; brainly.com/question/2491296