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3 years ago

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A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at random from the box. W

hat is the probability that both marbles are red?

1 answer:

Nata [24]3 years ago

7 0

I believe it's 2/10.

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A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

7 0

3 years ago

Solve the system of equations. y=-3x+4 -4x+y=-10

Angelina_Jolie [31]

Answer:

Step-by-step explanation:

In this particular case we have the following system of equations:

y

=

−

3

x

+

4

[

E

q

.

1

]

x

+

4

y

=

−

6

[

E

q

.

2

]

Substituting

[

E

q

.

1

]

in

[

E

q

.

2

]

:

x

+

4

(

−

3

x

+

4

)

=

−

6

Applying the distributive property on the left side:

x

−

12

x

+

16

=

−

6

Simplifying

:

−

11

x

=

−

22

Solving for

y

:

x

=

−

22

−

11

=

2

Substituting

x

=

2

in

[

E

q

.

1

]

:

y

=

−

3

(

2

)

+

4

=

−

2

Therefore

, the solutions are

x

=

2

and

y

=

−

2

7 0

3 years ago

Read 2 more answers

I don’t know where to start someone helpp

11111nata11111 [884]

Donald will have 20x+10 dollars

5 0

3 years ago

Read 2 more answers

Consider the figure.<br> What is JL?

lisov135 [29]

The answer for the above mentioned problem is JL = 12.5

Step by step explanation:

Given:

JM = 8

KM = 6

To Find:

JL = ?

Formula to be used:

$KM^2$ = JM x ML

In order to find " JL" we must first find "ML",

$KM^2$ = JM x ML

$6^2$ = 8 x ML

36 = 8 x ML

36/8 = ML

ML = 4.5

Now JL = 4.5+8

= 12.5

Thus the value of JL = 12.5

3 0

3 years ago

There are two similar purses. The blue purse has a volume of 837 cm? and the red purse has a volume of 248 cm3, If the width of

Sunny_sXe [5.5K]

The width of the blue purse that is similar to the red purse is approximately 50.6 cm.

<h3>How to Determine the Linear Measurement and Volume of Similar Solids?</h3>

If two solids, A and B, has a linear measure a and b respectively, and they are both similar to each other, the ratio of their volumes and their linear measures would be expressed as:

Volume of solid A/volume of solid B = a³/b³.

We are given two purses that are similar to each other:

Volume of Blue purse = 837 cm³

Volume of Red purse = 248 cm³

Width of Red purse = 15 cm

Let width of Blue purse be = x

Therefore we would have the following ratio:

Volume of blue purse/volume of red purse = (width of blue purse)³/(width of red purse)³

Plug in the values

837/248 = x/15

Cross multiply

(248)(x) = (837)(15)

248x = 112,555

Divide both sides by 248

248x/248 = 112,555/248

x = 50.6 cm

The width of the blue purse is approximately 50.6 cm.

Learn more about volume of similar solids on:

brainly.com/question/16599646

#SPJ1

3 0

1 year ago