Quentin Johnson
2022-01-19
Answered

What are the mean and standard deviation of a binomial probability distribution with n=12 and $p=\frac{3}{5}$ ?

You can still ask an expert for help

reinosodairyshm

Answered 2022-01-19
Author has **36** answers

Explanation:

Mean of a binomial probability distribution is given by np and standard deviation is given by$\sqrt{n}pq$ , where q=1-p.

In the given example,$np=12\cdot \frac{3}{5}=7.2,$

As$q=1-\frac{3}{5}=\frac{2}{5},\sqrt{n}pq=\sqrt{12\cdot \frac{3}{5}\cdot \frac{2}{5}}=\frac{1}{5}\cdot \sqrt{72}=6\frac{\sqrt{2}}{5}=1.697$

Hence mean is 7.2 and standard deviation is 1.697

Mean of a binomial probability distribution is given by np and standard deviation is given by

In the given example,

As

Hence mean is 7.2 and standard deviation is 1.697

Elois Puryear

Answered 2022-01-20
Author has **30** answers

The formula for the population mean is $\mu =n\cdot p$ , so therefore we get:

$\mu =n\cdot p$

$=12\cdot \frac{3}{5}$

=7.2

On the other hand, the variance is computed using the following formula:${\sigma}^{2}=np(1-p)$ . Therefore, the calculation goes like:

${\sigma}^{2}=np(1-p)$

$=12\cdot \frac{3}{5}(1-\frac{3}{5})$

=2.88

And finally, taking square root to the variance we get that the population standard deviation is:

$\sigma =\sqrt{{\sigma}^{2}}=\sqrt{2.88}=1.697$

=7.2

On the other hand, the variance is computed using the following formula:

=2.88

And finally, taking square root to the variance we get that the population standard deviation is:

asked 2021-03-18

A population of values has a normal distribution with

Find the probability that a single randomly selected value is between 133.6 and 134.1.

Write your answers as numbers accurate to 4 decimal places.

asked 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a

Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places

asked 2022-01-28

A population has a mean of 24.8 and a standard deviation of 4.2. If ${x}_{i}=19$ , what is the z-value?

asked 2021-06-02

The joint density of the random variables X and Y is given by

$f(x,y)=\{\begin{array}{ll}8xy& 0\le x\le 1,0\le y\le x\\ 0& otherwise\end{array}$

Find the marginal density of X

Find the marginal density of X

asked 2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=5 and $p=\frac{1}{32}$ ?

asked 2021-10-28

Suppose that X and Y are continuous random variables with joint pdf $f(x,y)={e}^{-(x+y)}0<x<\mathrm{\infty}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}0y\mathrm{\infty}$ and zero otherwise.

Find P(X+Y>3)

Find P(X+Y>3)

asked 2021-05-18

Find the expected values and variances of the exponential random variables with the density functions given below

$3{e}^{-3x}$