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2 years ago

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On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 y

ellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from that box, what is the probability that the marble selected will be purple?

1 answer:

klemol [59]2 years ago

4 0

Answer: Our required probability would be 0.35.

Step-by-step explanation:

Since we have given that

Number of boxes = 2

Number of purple marbles in Box A = 30

Number of yellow marbles in Box A = 20

Number of purple marbles in Box B = 15

Number of yellow marbles in Box B = 35

So, If Melanie randomly selects one of the boxes and then randomly selects one marble from that box.

Probability that the marble selected will be purple is given by

$\dfrac{1}{2}\times \dfrac{20}{50}+\dfrac{1}{2}\times \dfrac{15}{50}\\\\=\dfrac{1}{2}(\dfrac{20+15}{50})\\\\=\dfrac{1}{2}\times \dfrac{35}{50}\\\\=\dfrac{35}{100}\\\\=0.35$

Hence, our required probability would be 0.35.

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Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence in

seraphim [82]

Answer:

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

Step-by-step explanation:

Previous concepts

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".

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=13.625$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.669 represent the sample standard deviation

n=8 represent the sample size

Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

Since the confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.365$

Now we have everything in order to replace into formula (1):

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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2 years ago

A rectangle’s length is 2 units more than twice its width. Its area is 40 square units. The equation w(2w + 2) = 40 can be used

barxatty [35]

I hope this helps you

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2 years ago

Read 3 more answers

A project’s critical path is composed of activities A (variance .33), B (variance .67), C (variance .33), and D (variance .17).

julia-pushkina [17]

Answer:

The standard deviation on the critical path = 0.834

Step-by-step explanation:

Variance of activity A ( $V_{1}$ ) = 0.33

Variance of activity B ( $V_{2}$ ) = 0.67

Variance of activity C ( $V_{3}$ ) = 0.33

Variance of activity D ( $V_{4}$ ) = 0.17

Thus the standard deviation on the critical path ( $\alpha ^{2}$ ) = $V_{1} ^{2}$ + $V^2_{2}$ + $V^2_{3}$ + $V^2_{4}$

$\alpha ^{2}$ = $0.33^{2}$ + $0.67^{2}$ + $0.33^{2}$ + $0.17^{2}$

$\alpha ^{2}$ = 0.6956

$\alpha$ = 0.834

The standard deviation on the critical path = 0.834

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2 years ago

A formula for 6 gallon of light green paint use 3/8 gallons of white paint. Liam has 9/16 gallon of white paint. Does liam have

FromTheMoon [43]

Answer:

Yes he have enough white paint.

Step-by-step explanation:

We are given

6 gallons of light green paint use → $\frac{3}{8}$ gallons of white paint

using the unitary method

1 gallons of white paint → 6*8/3 gallons of light green paint

→ 16 gallons of light green paint

but Liam have 9/16 gallons of white paint

9/16 gallons of white paint → 16* 9/16 gallons of light green paint

→ 9 gallons of light green paint

Yes Liam have enough white paint to make 8 gallons of light green paint.

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The product of two ratio rational numbers is 48/5. If one of the rational number is 66/7, find the other rational number.

goldenfox [79]

Let x = the other rational number.

x(66/7) = (48/5)

Solve for x to find your answer.

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