Mathematics, 10.11.2020 17:20 nvmcneill

Assume that 25% of all households in Santa Clara county have a burglar alarm (population characteristic). A random sample of 200 Santa Clara county households is taken. What is the probability that between 20% (0.2) to 30% (0.3) of the households in the sample have a burglar alarm

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Answer from: lia3865

The probability is P( 0.2 < p < 0.3) = 0.89751

Step-by-step explanation:

From the question we are told that

The population proportion is p = 0.25

The sample size is n = 200

Generally given that the sample size is large the mean of this sampling distribution is mathematically represented as $\mu_{x} = p = 0.25$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{ \frac{ p (1- p ) }{n} }$

=> $\sigma = \sqrt{ \frac{ 0.25(1- 0.25 ) }{200} }$

=> $\sigma = 0.03062$

Generally the probability that between 20% (0.2) to 30% (0.3) of the households in the sample have a burglar alarm is mathematically represented as

$P( 0.2 < p < 0.3) = P(\frac{ 0.2 - 0.25}{ 0.03062 } < \frac{p- \mu_{x}}{\sigma } < \frac{ 0.2 - 0.25}{ 0.03062 } )$

$\frac{p -\mu}{\sigma } = Z (The \ standardized \ value\ of \ p )$

=> P( 0.2 < p < 0.3) = P(-1.6329 < Z

=> P( 0.2 < p < 0.3) = P( Z< 1.6329) - P( Z

From the z table the area under the normal curve to the left corresponding to 1.6329 and -1.6329 is

P( Z< 1.6329) = 0.94875

and

P( Z

P( 0.2 < p < 0.3) = 0.94875 - 0.051245

=> P( 0.2 < p < 0.3) = 0.89751

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

Answer from: Quest

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)

= sin(7pi/6 - 2pi/6)

= sin(5pi/6)

= sin(pi - pi/6)

= sin(pi/6)

= 1/2

sin 7pi/6 - sin pi/3

= sin (pi + pi/6) - sin pi/3

= -sin pi/6 - sin pi/3

= -1/2 - sqrt(3)/2

= -(1+sqrt(3))2

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