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A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with millimeters. A random sample of 15 rings has a mean diameter of x Overscript bar EndScripts equals 74.127. Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter. (b) Calculate the 95% one-sided lower confidence interval on the true mean piston diameter.

Respuesta :

Answer:

(a) 74.12633 mm ≤ μ ≤ 74.12767 mm

(b) μ ≥ 74.12649 mm

Step-by-step explanation:

Here we have;

Sample count, n = 15

Mean, [tex]\bar x[/tex] = 74.127 mm

Standard deviation, σ = 0.001 mm

(a) The confidence interval, CI is given as follows;

[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]

At 99%, z = ±2.575829

Therefore, the confidence interval is;

[tex]CI=74.127 - 2.575829 \times \frac{0.001}{\sqrt{15}} \leq \mu \leq 74.127 + 2.575829 \times \frac{0.001}{\sqrt{15}}[/tex]

74.12633 mm ≤ μ ≤ 74.12767 mm

(b) The lower confidence at 95% is given by;

z at 95% = 1.959964

[tex]CI=\bar{x} - z\frac{\sigma}{\sqrt{n}}[/tex]

or μ ≥ 74.12649 mm.

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