Abottling plant produces 1 liter bottles of soda. the actual distribution of volumes of soda dispensed to bottles is normal, with mean μ and standard deviation σ = 0.05 liter. we randomly select 6 bottles andmeasure the volume of soda in each. the results of these 6 measurements (all in liter units) are 1.05 1.04 1.01 1.06 0.94 0.99. based on these data, a 90% confidence interval for μ is

Given:

Standard deviation = 0.05

Mean = (1.05 + 1.04 + 1.01 + 1.06 + 0.94 + 0.99 / 6) = 1.015

n = 6

Confidence level = 90%

Z score for 90% = 1.645

Solution:

Formula is mean ± z (s / sqrt (n))

= 1.015 ± (1.645) (0.05/ sqrt (6)

= 1.015 ± (1.645) (0.020412414)

= 1.015 ± 0.033578421

= 0.9814 < x < 1.0486 is the confidence interval

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3