Please help with this

For a fair coin, suppose you toss the coin 100 times.

Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

$\mu = np = 100(0.5) = 50$ .

$\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5$

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is one subtracted by the p-value of Z when X = 66.5.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{66.5 - 50}{5}$

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

More can be learned about the normal distribution at brainly.com/question/4079902

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6 0

1 year ago

What’s 3.984 + 17 ? Help

Korolek [52]

Answer:

20.984

Step-by-step explanation:

Just do:

3.984

+17.000

17 plus 3 equals 20 and .984 + 000 is .984

So your answer is 20.984

8 0

3 years ago

The equations in this sytem were added to solve for x. What is the value of x?

son4ous [18]

Question:

The equations in this system were added to solve for x. What is the value of x? -2x+y=8 5x-y=-5 3x=3

Options:

x = negative 3

x = negative 1

x = 1

x = 3

Answer:

The value of x is 1

Solution:

Given system of equations are:

-2x + y = 8 ------- eqn 1

5x - y = -5 ------- eqn 2

The above equations are added to solve for "x"

Add eqn 1 and eqn 2

-2x + y + 5x - y = 8 - 5

Combine the like terms

-2x + 5x + y - y = 3

Add the like terms

3x + 0 = 3

3x = 3

Divide both sides of equation by 3

x = 1

Thus the value of x is 1

8 0

3 years ago

Read 2 more answers

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distr

Tanya [424]

Complete Question

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test $H_o : p = 0.28$ vs $H a : p < 0.28$ when the sample has n 900 , and $\^ p = 0.216$ with $SE= 0.01$ . Find the value of the standardized z -test statistic. Round your answer to two decimal places.