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3 years ago

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Hank has 52 marbles. Divide them into 2 groups so that for every 6 marbles in the first group there are 7 marbles in the second

group.

1 answer:

Vikki [24]3 years ago

8 0

24 marbles in the first group

28 marbles in the second group

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The amount that two groups of students spent on snacks in one day is shown in the dot plots below.

Ymorist [56]

Answer:

1. The mean for Group A is less than the mean for Group B

2. The median for Group A is less than the median for Group B.

3. The mode for Group A is less than the mode for Group B.

Step-by-step explanation:

1. To find the mean for Group A, you use the formula: Total sum/Total frequency.

To find the total sum, you multiply the frequency(how many times the given number is repeated) with the given numbers.

0 × 0 = 0

1 × 5 = 5

2 × 4 = 8

3 × 1 = 3

4 × 0 = 0

5 × 0 = 0

Total Sum: 5 + 8 + 3 = 16

Total frequency: 5 + 4+ 1 = 10

$\frac{16}{10}$ = 1.6

To find the mean for Group B, you repeat everything above.

0 × 0 = 0

1 × 3 = 3

2 × 2 = 4

3 × 4 = 12

4 × 0 = 0

5 × 1 = 5

Total Sum: 3 + 4 + 12 + 5 = 24

Total frequency: 3 + 2 + 4 + 1 = 10

$\frac{24}{10}$ = 2.4

2. I can't explain it but I'm certain that it is correct.

3. The most repeated number for Group A is 1, it is repeated 5 times, while the most repeated number in Group B is 3, it is repeated 4 times.

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3 years ago

There is a mid ocean ridge between South America and Africa causing the two continents to drift away from each other. South Amer

Oksanka [162]

Answer:

2.5 cm/year

Step-by-step explanation:

Just divide the total distance, 250 cm, by the years, 100, 250/100 = 2.5, the rate of the contintents drifting away is 2.5 cm per year, 2.5 cm/year

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3 years ago

Llana [10]

The answer to this question will be f

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3 years ago

India vs England test series in Nottingham<br>I will cheer for India because I am an Indian<br>

Alex_Xolod [135]

Answer:

Is this suppose to be math question??

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3 years ago

Read 2 more answers

An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a

LekaFEV [45]

Let Xb be the number of reservations that are accommodated. Xb has the binomial distribution with n trials and success probability p = 0.94

In general, if X has the binomial distribution with n trials and a success probability of p then
P[Xb = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[Xb = x] = 0 for any other value of x.

To use the normal approximation to the binomial you must first validate that you have more than 10 expected successes and 10 expected failures. In other words, you need to have n * p > 10 and n * (1-p) > 10.

Some authors will say you only need 5 expected successes and 5 expected failures to use this approximation. If you are working towards the center of the distribution then this condition should be sufficient. However, the approximations in the tails of the distribution will be weaker espeically if the success probability is low or high. Using 10 expected successes and 10 expected failures is a more conservative approach but will allow for better approximations especially when p is small or p is large.

If Xb ~ Binomial(n, p) then we can approximate probabilities using the normal distribution where Xn is normal with mean μ = n * p, variance σ² = n * p * (1-p), and standard deviation σ

I have noted two different notations for the Normal distribution, one using the variance and one using the standard deviation. In most textbooks and in most of the literature, the parameters used to denote the Normal distribution are the mean and the variance. In most software programs, the standard notation is to use the mean and the standard deviation.

The probabilities are approximated using a continuity correction. We need to use a continuity correction because we are estimating discrete probabilities with a continuous distribution. The best way to make sure you use the correct continuity correction is to draw out a small histogram of the binomial distribution and shade in the values you need. The continuity correction accounts for the area of the boxes that would be missing or would be extra under the normal curve.

P( Xb < x) ≈ P( Xn < (x - 0.5) )
P( Xb > x) ≈ P( Xn > (x + 0.5) )
P( Xb ≤ x) ≈ P( Xn ≤ (x + 0.5) )
P( Xb ≥ x) ≈ P( Xn ≥ (x - 0.5) )
P( Xb = x) ≈ P( (x - 0.5) < Xn < (x + 0.5) )
P( a ≤ Xb ≤ b ) ≈ P( (a - 0.5) < Xn < (b + 0.5) )
P( a ≤ Xb < b ) ≈ P( (a - 0.5) < Xn < (b - 0.5) )
P( a < Xb ≤ b ) ≈ P( (a + 0.5) < Xn < (b + 0.5) )
P( a < Xb < b ) ≈ P( (a + 0.5) < Xn < (b - 0.5) )

In the work that follows X has the binomial distribution, Xn has the normal distribution and Z has the standard normal distribution.

Remember that for any normal random variable Xn, you can transform it into standard units via: Z = (Xn - μ ) / σ

In this question Xn ~ Normal(μ = 0.94 , σ = sqrt(0.94 * n * 0.06) )

Find n such that:

P(Xb ≤ 160) ≥ 0.95

approximate using the Normal distribution
P(Xn ≤ 160.5) ≥ 0.95

P( Z ≤ (160.5 - 0.94 * n) / sqrt(0.94 * n * 0.06)) ≥ 0.95

P( Z < 1.96 ) ≥ 0.95

so solve this equation for n

(160.5 - 0.94 * n) / sqrt(0.94 * n * 0.06) = 1.96

n = 164.396

n must be integer valued so take the ceiling and you have:

n = 165.

The air line can sell 165 tickets for the flight and accommodate all reservates at least 95% of the time

If you can understand that...

7 0

3 years ago