Answer:
[3.75 years, 5.45 years]
Step-by-step explanation:
The 90% confidence interval is given by the interval
![\large [\bar x-t^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]](https://tex.z-dn.net/?f=%5Clarge%20%5B%5Cbar%20x-t%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%2C%20%5Cbar%20x%2Bt%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%5D)
where
<em>
is the sample mean </em>
<em>s is the sample standard deviation </em>
<em>n is the sample size
</em>
is the 0.05 (5%) both-sided (**) critical value for <em>the Student's t-distribution with 19 degrees of freedom (sample size -1), which is an approximation to the Normal distribution for small samples (n≤ 30).
</em>
Either by using a table or the computer, we find
and our 90% confidence interval is
![\large [4.6-1.729*\frac{2.2}{\sqrt{20}}, 4.6+1.729*\frac{2.2}{\sqrt{20}}]=\boxed{[3.75,5.45]}](https://tex.z-dn.net/?f=%5Clarge%20%5B4.6-1.729%2A%5Cfrac%7B2.2%7D%7B%5Csqrt%7B20%7D%7D%2C%204.6%2B1.729%2A%5Cfrac%7B2.2%7D%7B%5Csqrt%7B20%7D%7D%5D%3D%5Cboxed%7B%5B3.75%2C5.45%5D%7D)
(**) 5% of the area to the left of 
and 5% to right of for a total of 90% inside the interval ![\large [-t^*,+t^*]](https://tex.z-dn.net/?f=%5Clarge%20%5B-t%5E%2A%2C%2Bt%5E%2A%5D)
Answer:
2.7 x 10⁻³
6.1 x 10⁵
9.582 x 10⁶
Step-by-step explanation:
The first digits part should be more or equal 1 and less 10
Reorder the right side of the equation to match the vertex form of a parabola.
y
=
(
x
−
4
)
2
−
11
y
=
(
x
-
4
)
2
-
11
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
y
=
a
(
x
-
h
)
2
+
k
, to determine the values of
