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.

(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, = 74.127 mm

Standard deviation, σ = 0.001 mm

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

At 99%, z = ±2.575829

Therefore, the confidence interval is;

74.12633 mm ≤ μ ≤ 74.12767 mm

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

z at 95% = 1.959964

or μ ≥ 74.12649 mm.

hi there!

step-by-step explanation:

a roof pitch is basically for every inch rise there is 12 inches run.

the height of the roof is also known as the rafter.

formula: rafter^2 = rise^2 + run^2

rafter^2 = 5^2 + 12^2

rafter^2 = 25 + 144

rafter ^2 = 169"^2

the height of the roof from the lowest point to the highest point is 169"^2.

hope this : )