Mathematics, 02.10.2019 01:30 bjbailey1561

The bureau of alcohol, tobacco, and firearms (batf) has been concerned about lead levels in california wines. in a previous testing of wine specimens, lead levels ranging from 50 to 700 parts per billion were recorded. how many wine specimens should be tested if the batf wishes to estimate the true mean lead level for california wines to within 10 parts per billion with 95% confidence?

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Answer from: robbiegfarmer

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

$\sigma = \sqrt{\frac{(b - a)^2}{12}}$

In this problem, a = 50, b = 700 , thus, the estimate is:

$\sigma = \sqrt{\frac{(700 - 50)^2}{12}} = 187.64$

The margin of error of a z-confidence interval is given by:

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

In which:

z is the critical value. $\sigma$ is the population standard deviation. n is the sample size.

The first step is finding the critical value, which is z with a p-value of $\frac{1 + \alpha}{2}$ , in which $\alpha$ is the confidence level.

In this problem, $\alpha = 0.95$ , thus, z with a p-value of $\frac{1 + 0.95}{2} = 0.975$ , which means that it is z = 1.96.

Estimate of the standard deviation is of 187.64, thus, $\sigma = 187.64$ .

We want the sample for a margin of error of 10, thus, we have to solve for n when M = 10 . Then:

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

$10 = 1.96\frac{187.64}{\sqrt{n}}$

$10\sqrt{n} = 1.96(187.64)$

Simplifying by 10:

$\sqrt{n} = 0.196(187.64)$

$(\sqrt{n})^2 = [0.196(187.64)]^2$

n = 1352.6

Rounding up:

1353 specimens should be tested.

A similar problem is given at link

Answer from: lisnel

1015

Step-by-step explanation:

Given :In a previous testing of wine specimens, lead levels ranging from 50 to 700 parts per billion were recorded.

Here , Range = 700-50=650 [∵ Range = Max-Min]

According to the thumb rule , the range is approximately 4 times the standard deviation.

Let $\sigma$ be the standard deviation, then

$\text{Range}\approx4\times\sigma\\\\\Rightarrow\ \sigma\approx\dfrac{\text{Range}}{4}=\dfrac{650}{4}=162.5$

Thus, $\sigma\approx162.5$

For confidence interval of 95% , the critical z value = $z_{\alpha/2}=1.96$

Formula to find the sample size : $(\dfrac{z_{\alpha/2}\ \sigma}{E})^2$

Now, for the margin of error of E= $\pm 10$ , we have

$(\dfrac{1.96\times162.5}{10})^2=1014.4225\approx1015$

Hence, the required sample size = 1015

Answer from: Quest

Ithink the answer should be b.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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