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spayn [35]
3 years ago
14

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible c

ombinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?
Mathematics
1 answer:
lutik1710 [3]3 years ago
8 0

Answer:

Tamara should expect the sum of the two cubes to be equal to 5 20 times.

Step-by-step explanation:

The sample space of rolling a number cube are:

S = {1, 2, 3, 4, 5, 6}

If two such cubes are rolled together, then the sum of the two cubes will be 5 for the combinations below:

S₁ = {(1, 4), (2, 3), (3, 2) and (4, 1)}

The total number of outcomes will be, <em>N</em> = 36.

Compute the probability that the sum of rolling two numbered cubes as follows:

P(\text{Sum}=5)=\frac{4}{36}=\frac{1}{9}

Let <em>X</em> = number of time the sum of the two numbers on two cubes is 5.

Two numbered cubes are rolled <em>n</em> = 180 times.

The event of getting a sum of 5 in independent of the other results.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 180 and <em>p</em> = \frac{1}{9}.

The expected value of <em>X</em> is:

E(X)=np

Compute the expected number of times Tamara expects the sum of the two cubes to be equal to 5 as follow:

E(X)=np\\=180\times \frac{1}{9}\\=20

Thus, Tamara should expect the sum of the two cubes to be equal to 5 20 times.

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Arlo rolls a number cube three times. What is the chance the number cube
OlgaM077 [116]

Answer:

Probability = 1/8.

Step-by-step explanation:

A number cube has six sides. Each side has a number from 1 to 6. This means that there are 3 even numbers (2, 4, and 6) and 3 odd numbers (1, 3, and 5). Therefore:

P(number cube lands on an even number after roll) = Number of even numbers/Number of total numbers. = 3/6 = 1/2.

Since the cube has to be rolled three times, the probability will be multiplied 3 times (assuming that each roll in independent of each other). Therefore:

P(number cube lands on an even number 3 times after roll) = 1/2 * 1/2 * 1/2 = 1/8.

Therefore, the answer is 1/8!!!

5 0
2 years ago
Compatible numbers for 2.4 and -0.18 are 2.5 and -0.2. What is the estimation of the product of (2.4)(-0.18)
Roman55 [17]

Answer:

-0.5

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What could be the next line in the solution of the equation 3 (x - 2) = 15 ?
Ket [755]
X = 7 is the answer
5 0
2 years ago
Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math
bekas [8.4K]

Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

6 0
3 years ago
Please and thank you
KatRina [158]

Answer:

\huge\boxed{\sf x = 4}

Step-by-step explanation:

If the given polygon is a regular polygon, its sides are equal.

This means:

x^2+4=x^2+x

Subtract x^2 to both sides

4 = x

OR

x = 4

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
8 0
2 years ago
Read 2 more answers
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