# In a binomial distribution, the symbols p and q are used to represent probabilities. Tell what the numerical relationship between p and q is.

Question
Binomial probability
In a binomial distribution, the symbols p and q are used to represent probabilities. Tell what the numerical relationship between p and q is.

2020-12-04
The numerical relationship is that p is the probability of success and q is the probability of failure. The sum of p and q is 1, or p + q = 1, or p = q – 1, or q = 1 – p.

### Relevant Questions

1) State the formula for the Binomial Probability Distribution, also state the domain. 2) Tell what the requirement for the Binomial experiment are. 3) List both formulas for calculating the mean of a Binomial Probability Distribution. 4) List the formulas for the standard deviation of a Binomial Probability Distribution.
Two stationary point charges +3 nC and + 2nC are separated bya distance of 50cm. An electron is released from rest at a pointmidway between the two charges and moves along the line connectingthe two charges. What is the speed of the electron when it is 10cmfrom +3nC charge?
Besides the hints I'd like to ask you to give me numericalsolution so I can verify my answer later on. It would be nice ifyou could write it out, but a numerical anser would be fine alongwith the hint how to get there.

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

Convert the binomial probability to a normal distribution probability using continuity correction. $$P(x > 14)$$.

Compute the distribution of X+Y in the following cases:
X and Y are independent binomial random variables with parameters (n,p) and (m,p).

Compute the following binomial probabilities directly from the formula for $$b(x, n, p)$$:

a) $$b(3,\ 8,\ 0.6)$$

b) $$b(5,\ 8,\ 0.6)$$

c) $$\displaystyle{P}{\left({3}≤{X}≤{5}\right)}$$

when $$n = 8$$ and $$p = 0.6$$

d)$$\displaystyle{P}{\left({1}≤{X}\right)}$$ when $$n = 12$$ and $$p = 0.1$$

If x is a binomial random variable, find the probabilities below by using the binomial probability table.

a) $$P(x < 11)\ for\ n = 15, p = 0.1$$

b) $$P(x \geq 11)\ for\ n = 25, p = 0.4$$

c) $$P(x = 2)\ for\ n = 20, p = 0.6$$

$$\begin{array}{|c|c|} \hline t & с\\ \hline 1 & 7 \\ \hline 2&14\\ \hline 3&21\\ \hline 4&28\\ \hline \end{array}$$