2.5 × 30 = ___________ tenths × 30 = _____

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

3 years ago

PLSSS HELP DUE IN 20 MINUTES WILL GIVE BRAINLIEST THANKS AND 5 STARSS PLSSSS OMG

Zina [86]

Answer:

x=10

Step-by-step explanation:

There's an attached photo here

7 0

3 years ago

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Can the formula F=ma be a direct variation equation? If so, which variable would have to be held constant?

ANEK [815]

Yes it can be a direct variation. it follows the form y = kx
The only variable that cannot be held constant is F, but we can hold the mass constant and vary the acceleration OR we can hold the acceleration constant and vary the mass. Either one would work, but the easiest would be to vary the mass and hold the acceleration constant since we are all pulled by the same action gravity

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3 years ago

The value of a professional basketball player's autograph rose 30% in the last year. It is now worth $325.00. What was it worth

ANEK [815]

$227.50. First, you convert 30% into a decimal: 0.30. Then, you multiply 325.00 by 0.30. This equals 97.50. 97.50 is 30% of 325, so you need to subtract 97.50 from 325.00. This equals $227.50.

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4 years ago

(8y-1)-4[(7y+5)-3(2y-9)

alexdok [17]

8y-1-28y-20-6y+27
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3 years ago

2.5 × 30 = ___________ tenths × 30 = ______

2.5 × 30 = _____ tenths × 30 =