Amanufacturer produces piston rings for an automobile engine. it is known that ring diameter is normally distributed with σ=0.001 millimeters. a random sample of 15 rings has a mean diameter of x¯=74.021. 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. round your answers to 3 decimal places.

The confidence interval for population mean is given by :-

                  (1)

, where = sample mean

z* = critical value.

SE = standard error

and , = population standard deviation.

n= sample size.

As per given , we have

n= 15

It is known that ring diameter is normally distributed.

By z-table ,

The critical value for 95% confidence  = z*= 1.96

A 99% two-sided confidence interval on the true mean piston diameter :

    (using (1))

 [Rounded to three decimal places]

∴  A 99% two-sided confidence interval on the true mean piston diameter  = (74.020, 74.022)

By z-table ,

The critical value for 95% confidence  = z*= 1.96

A 95% lower confidence bound on the true mean piston diameter:

   (using (1))

[Rounded to three decimal places]

∴  A 95% lower confidence bound on the true mean piston diameter= 74.020

what does x eaqual

step-by-step explanation: