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2 years ago

6

Samantha has a bag of 5 different colored marbles. She randomly picks a marble from the bag, records the color, and returns it t

o the bag before picking another marble. What is the probability that she picks a blue marble three times in a row?

1 answer:

skelet666 [1.2K]2 years ago

3 0

Since there can only be one blue marble out of five marbles,
1/5 x 1/5 x 1/5 = 0.008 or 0.8%

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Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in

Hitman42 [59]

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of Americans who decide to not go to college = 48%

n = sample of American adults = 331

p = population proportion of Americans who decide to not go to

college because they cannot afford it

<em>Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.</em>

<em />

<u>So, 90% confidence interval for the population proportion, p is ;</u>

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\hat p-p$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

<u>90% confidence interval for p</u> = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ , $0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ ]

= [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

$0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }$

$\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}$

$\sqrt{n}$ = 54.79

n = $54.79^{2}$

n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

5 0

2 years ago

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

Sav [38]

Answer:

10.12 $m^{3}$

Step-by-step explanation:

Given:

0.07 cm thick = 0.007m and it is dr (the change in radius)

As we know that, the volume of a hemispherical dome with diameter 48 m is:

V = $\frac{2}{3}$ π $r^{3}$

Take the derivative of V we have:

$\frac{dV}{dr}$ = 2π $r^{2}$

<=> dV = 2π $r^{2}$ *dr

<=> dV = 2π* $48^{2}$ *0.0007 = 10.12 $m^{3}$

Hope it will find you well.

6 0

2 years ago

Read 2 more answers

-3 \cdot f(-8) + 7 \cdot g(2) =−3⋅f(−8)+7⋅g(2)=minus, 3, dot, f, left parenthesis, minus, 8, right parenthesis, plus, 7, dot, g,

dsp73

Answer:

-22

Step-by-step explanation:

The graph from which the information is to be read is attached below.

We want to find the value of −3⋅f(−8)+7⋅g(2).

From the graph:

f(-8)=-2
g(2)=-4

Therefore:

−3⋅f(−8)+7⋅g(2)=−3(-2)+7(-4)

=6-28

=-22

−3⋅f(−8)+7⋅g(2)=-22

3 0

2 years ago

A falcon flies 800,000 meters in 4 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represen

photoshop1234 [79]

Answer:

a. r=d/t b. 800000/4=200,000 c.800/2=200 d.not sure km are used more often as theyre simpler to use but there is not much that i am basing this off of

Step-by-step explanation:

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2 years ago

The spelling contest awards four prizes Tim,Sam,Jen, and Kate all made it to the final round. In how many ways can first, second

topjm [15]

It is the 3 one correct me if im wrong

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2 years ago