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<h2>Answer with explanation:</h2>
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
Compound interest:
where
is the amount you start with, 
is the interest rate, 
is the number of times interest is compounded per year, and 
is amount of time that passes.
where