Evaluate [6 - (5 - 6(5 - 7) + 3)] + 3

A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

7 0

2 years ago

O GRAPHIS,

bezimeni [28]

Answer:

y = 3x - 16

Step-by-step explanation:

I just graphed the slope and went down 3 over to the left 1 and I found 16 was the intercept

3 0

3 years ago

Solve for x. Leave your answer as a fraction.<br> 4x-2/5 = 2/7

Fed [463]

Answer: x= 6/35

Explanation

8 0

3 years ago

Which is the x-intercept of the graph of the equation y=3x−9?

padilas [110]

Y=3x−9

y=3(0)-9

y=9

Now plug in y to solve for x.

y=3x−9

9=3x-9

18=3x

6=x

The x-intercept is (6,0)

3 0

2 years ago

What are the Rates of Change and the initial values to these? If you don't have the answer I'll take an explanation on how to do

gogolik [260]

Step-by-step explanation:

So, a coordinate plane is made out of two axis, the x and the y. Through these, we have grid squares on the plane showing points. So, each square would be one point. To find the <u>rate of change, or slope,</u> you would have to use the formula:

y(#2) - y(#1)

------------------ = Divided by

x(#2) - y(#1)

This formula will calculate the rate of change. I will do the first one for you as follows.

The first point I would find would be (1,3). 1 space on the X-axis, 3 on the Y-axis.

To write a ordered pair to represent the point on the plane, use the (X,Y).

Then, I'd find the second point.

Following the second point, I would do the equation like so.

y(2) - 3

-----------------

x(2) - 1

See, I used the first points given as the last X and Y variables in the formula.

Hope this helps you out!

4 0

2 years ago