Question

use ( n = 6 ) and ( p = 0.5 ) to complete parts (a) through (d) below.
(a) construct a binomial probability distribution with the given parameters.

( x )	( p(x) )
1	0.0938
2	0.2344
3	0.3125
4	0.2344
5	0.0938
6	0.0156

(round to four decimal places as needed.)
(b) compute the mean and standard deviation of the random variable using ( mu_x=sumxcdot p(x) ) and ( sigma_x=sqrt{sumx^2cdot p(x)-mu_x^2} )
( mu_x = 3.00 ) (round to two decimal places as needed.)
( sigma_x=square ) (round to two decimal places as needed.)

Explanation:

Step1: Calculate \(\sum x^{2}\cdot P(x)\)

$$
LATEXBLOCK0
$$

Step2: Calculate \(\mu_{x}\)

We know \(\mu_{x}=\sum x\cdot P(x)\)

$$
LATEXBLOCK1
$$

Step3: Calculate \(\sigma_{x}\)

Use the formula \(\sigma_{x}=\sqrt{\sum x^{2}\cdot P(x)-\mu_{x}^{2}}\)
Substitute \(\sum x^{2}\cdot P(x) = 10.955\) and \(\mu_{x}=3\)

$$
LATEXBLOCK2
$$

Answer:

\(\sigma_{x}\approx1.40\)