<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
![\overline{x}=74.021](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D74.021)
![\sigma=0.001](https://tex.z-dn.net/?f=%5Csigma%3D0.001)
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))
![74.021\pm 0.000665120624](https://tex.z-dn.net/?f=74.021%5Cpm%200.000665120624)
[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
Answer:
12 x 24 = 288
32 - 24 = 8
8 x 12 = 96
96 divided by 2 = 48
288 + 48 = 336 ft2 is your answer.
Answer:96.97
Step-by-step explanation:
Given
mean height of women ![\mu _w=64](https://tex.z-dn.net/?f=%5Cmu%20_w%3D64)
Standard deviation of height ![\sigma _w=2.82](https://tex.z-dn.net/?f=%5Csigma%20_w%3D2.82)
mean height of men ![\mu _=69.3](https://tex.z-dn.net/?f=%5Cmu%20_%3D69.3)
Standard deviation of height ![\sigma _m=2.71](https://tex.z-dn.net/?f=%5Csigma%20_m%3D2.71)
P![\left ( X](https://tex.z-dn.net/?f=%5Cleft%20%28%20X%3C69.3%5Cright%20%29)
P![\left ( \frac{x-\mu _w}{\sigma _w}\right )](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bx-%5Cmu%20_w%7D%7B%5Csigma%20_w%7D%5Cright%20%29%3CP%5Cleft%20%28%20%5Cfrac%7B69.3-64%7D%7B2.82%7D%5Cright%20%29)
P![\left ( Z](https://tex.z-dn.net/?f=%5Cleft%20%28%20Z%3C1.8794%5Cright%20%29)
i.e. 0.9697=96.97 %
The observatory telescope has 22 times the magnifying power compared to the small telescope.
Data;
- small telescope = 150 times
- large telescope = 3300
<h3>Division of Numbers</h3>
To solve this question, we have to divide the large telescope by the small telescope to calculate it's magnifying power.
![x = \frac{3300}{150}=22](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3300%7D%7B150%7D%3D22)
The magnification of the observatory telescope is 22 times greater or larger than the small telescope.
Learn more on division of numbers here;
brainly.com/question/7068223