Mathematics, 03.08.2019 06:10, ashgold324

Seeclear windows makes windows for use in homes and commercial buildings. the standards for glass thickness call for the glass to average 0.375 inches with a standard deviation equal to 0.050 inch. suppose a random sample of nequals50 windows yields a sample mean of 0.392 inches. what is the probability if the windows meet the standards?

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answered: bliss6115

The probability if the windows meet the standards is 0.016.

Given

The standards for glass thickness call for the glass to average 0.375 inches with a standard deviation equal to 0.050 inches.

Suppose a random sample of nequals50 windows yields a sample mean of 0.392 inches.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The value of probability if the windows meet the standards is given by;

$\rm Z = \dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n} }}\\\\$

Substitute all the values in the formula;

$\rm Z = \dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n} }}\\\\ \rm Z = \dfrac{0.392-0.375}{\dfrac{0.050}{\sqrt{50} }}\\\\ Z = \dfrac{0.392-0.375}{0.050} \times {\sqrt{50} }\\\\Z= \dfrac{0.017}{0.050} \times 7.07\\\\Z=0.34 \times 7.07\\\\Z=2.40$

By using a standard normal distribution table, the p-value is 0.016.

Hence, the probability if the windows meet the standards is 0.016.

To know more about probability click the link given below.

link

answered: aatharris21

0.0164

Step-by-step explanation:

Given : The standards for glass thickness call for the glass to average $\mu=\text{ 0.375 inches}$ with a standard deviation 0 $\sigma=\text{ 0.050 inch}$ .

$H_0:\mu=0.375\\\\H_a:\mu\neq0.375$

Since the alternative hypothesis is two-tailed , so the test is two-tailed test.

Sample size : n=50 , a large sample ( n>30) so we use z-test.

Sample mean :- $\overline{x}=0.392$

We assume its a normal distribution.

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$z=\dfrac{0.392-0.375}{\dfrac{0.050}{\sqrt{50}}}\approx2.40$

By using standard normal distribution table , the p-value =

$0.0163951\approx0.0164$

Thus, the probability if the windows meet the standards = 0.0164

answered: Guest

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

answered: Guest

1/5 i hope this

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Seeclear windows makes windows for use in homes and commercial buildings. the standards for glass th...