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3 years ago

The results of rolling a 6-sided die 120 times are given in the table below.

Mathematics

1 answer:

Bas_tet [7]3 years ago

5 0

Step-by-step explanation:

According to the results of rolling a 6-sided die 120 times, we have:

Rolling a 2:

Experimental = 15/120 = 1/8 = 0.125 = 12.5%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1:

Experimental = 18/120 = 3/20 = 0.15 = 15%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1 or 6:

Experimental = 18/120 + 20/120 = 38/120 = 19/60= 0.3167 = 31.67%

Theoretical = 20/120 + 20/120 = 40/120 = 1/3 = 0.3333 = 33.33%

Step-by-step explanation:

1. First of all, let's recall what is the difference between experimental and theoretical probability of an event.

The experimental probability is the result of an experiment, and the theoretical probability is based on the mathematical model developed in the theory of probability. In simple words, the most important difference is that the experimental probability is based on what actually happens and the theoretical probability on what is expected to happen.

The accuracy of the results of the experiments depends directly on the sample size of the experiment and the accuracy is greater when the sample size is larger.

For this particular event the theoretical probability is the same for rolling each number of the die, 1/6 or 16.67%

Now, let's complete the answer this way:

Rolling a 2:

Experimental = 15/120 = 1/8 = 0.125 = 12.5%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1:

Experimental = 18/120 = 3/20 = 0.15 = 15%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1 or 6:

Experimental = 18/120 + 20/120 = 38/120 = 19/60= 0.3167 = 31.67%

Theoretical = 20/120 + 20/120 = 40/120 = 1/3 = 0.3333 = 33.33%

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Answer:

x = 3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

(3)(1)+2x=6

Step 1: Simplify both sides of the equation.

(3)(1)+2x=6

3+2x=6

2x+3=6

Step 2: Subtract 3 from both sides.

2x+3−3=6−3

2x=3

Step 3: Divide both sides by 2.

2x/2 3/2

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3 years ago

If f(x) = 3x5 + 4x3 + 3, then what is the remainder when f(x) is divided by<br> x - 3?

VikaD [51]

Answer:

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Step-by-step explanation:

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3 years ago

Verify sin^4 x - sin^2 x = cos^4 x - cos^2 x is an identity

Citrus2011 [14]

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2

sin(x)^2 = 1 - cos(x)^2:

sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

-(1 - cos(x)^2) = cos(x)^2 - 1:

cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2

sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:

-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2

(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:

cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

The left hand side and right hand side are identical:

Answer: (identity has been verified)

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3 years ago

I NEED ANSWER ASAP/ WILL GET 20 PTS

ki77a [65]

Answer: A. (-8,-3)

Step-by-step explanation:

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4 0

3 years ago

in a program designed to help patients stop smoking 232 patients were given sustained care and 84.9% of them were no longer smok

grandymaker [24]

Answer:

$z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869$

$p_v =2*P(Z>1.869)=0.0616$

If we compare the p value obtained and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .

Step-by-step explanation:

1) Data given and notation

n=232 represent the random sample taken

X represent the adults were no longer smoking after one month

$\hat p=0.849$ estimated proportion of adults were no longer smoking after one month

$p_o=0.80$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:

Null hypothesis: $p=0.8$

Alternative hypothesis: $p \neq 0.8$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z>1.869)=0.0616$

6 0

3 years ago