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olga_2 [115]
2 years ago
8

Probability and Playing Cards

Mathematics
1 answer:
vodomira [7]2 years ago
4 0

Answer:

do the calculation below

Step-by-step explanation:

(4/52 ) *(3/51)

leave a comment if you need more help

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Allen�s hummingbird (Selasphorus sasin ) has been studied by zoologist Bill Alther A small group of 15 Allen� s hummingbirds has
Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= <u> X[bar] - μ </u>~ N(0;1)

       σ/√n

The formula for the interval is:

X[bar] ± Z_{1- \alpha /2} * (σ/√n)

Z_{1- \alpha /2}= Z_{0.90} = 1.28

3.15 ± 1.28 * (0.33/√15)

[3.04; 3.26]gr

The margin of error (d) of a confidence interval is hal its amplitude (a)

a= Upper bond - Lower bond

d= (Upper bond - Lower bond)/2

d= \frac{(3.26-3.04)}{2} = 0.11

2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= Z_{1- \alpha /2} * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= Z_{1- \alpha /2} * (σ/√n)

\frac{d}{Z_{1- \alpha /2}}= σ/√n

√n * \frac{d}{Z_{1- \alpha /2}}= σ

√n = σ * \frac{Z_1- \alpha /2}{d}

n = (σ * \frac{Z_1- \alpha /2}{d})²

n=  (0.33 * \frac{1.28}{0.08})²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

4 0
3 years ago
What does -8(6x - 2) equal? How do I get my answer?
Free_Kalibri [48]

Answer:

-48x+16

Step-by-step explanation:

-8(6x - 2) first multiply each term in the parentheses by 8 to get -8x6x-8x(-2) and calculate the product to get your answer which is -48x+16

7 0
2 years ago
Read 2 more answers
I need help please!!
Alex73 [517]

Answer:

Sorry I could only find the answer to the second part.

y=56x

6 0
3 years ago
Factor -1/3 out of -1/3x-12
strojnjashka [21]
-\frac{1}{3}x-12\ \ \ | put\ -\frac{1}{3}\ in\ front\ of\ the\ bracket\\\\&#10;-\frac{1}{3}(x+36)\\\\&#10;Solution\ is\ -\frac{1}{3}(x+36)
5 0
3 years ago
olive bought 36 potatoes plants. She planted them in her garden in 4 even rows. Wild animals ate a row. 5 plants were eaten by s
almond37 [142]
If there are 36 potato plants, and they are in 4 even rows, that means that there is 9 in each column because 9 x 4 is 36. Since 7 of them were eaten by the sheep and the goat, that means that there are 2 leftover in that row that the sheep and goat got to since 9-7 is 2.
5 0
3 years ago
Read 2 more answers
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