Answer:
The value of is 10º.
Step-by-step explanation:
From Euclidean Geometry we remember that the sum of internal angles within a triangle equals to 180º. We present the resulting triangle after applying some geometric handling in the image attached below. Then, the triangle satisfies the following equation:
(1)
The value of is 10º.
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