Question

2 Use n - 10 and p 05 to complete parts (a) through (d) below (a) Construct a binomial probability distribution with the given 10 Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random vanable using μ,-Jr. P(x) and -(Round to two decmal places as needed ) Round to two decimal places as needed.) P,-- -fp(1-p) (c) Compute the mean and standard deviation, using μ,-np and (Round to two decimal places as needed.) (Round to two decimal places as needed) (d) Draw a graph of the probability distribution and comment on its shape. Which graph below shows the probability distribution? OB. Ос. D. Pix) Px) Px) P(x) 0.5 025 246 810 2 4 6 810 0246810 0246 810 The binomial probability distribution is (1)_ (1) O skewed left O skewed right O symmetric. O bimodal.

Answer 1

2. Since P=0.5 and n=10 hence using binomial probability formula as

P (k successes in n trials) = (、. )pkqn_k p*q n = number of trials k = number of successes p = probability of success in one trial q = 1 – p = probability of failure in one trial

(a) Hence using formula

X	P(X)
0	0.0010
1	0.0098
2	0.0439
3	0.1172
4	0.2051
5	0.2461
6	0.2051
7	0.1172
8	0.0439
9	0.0098
10	0.0010

(b) Using formula $\mu_{x}=\sum [x*P(x)]$

now

X	P(X)	X*P(X)
0	0.0010	0
1	0.0098	0.0098
2	0.0439	0.0878
3	0.1172	0.3516
4	0.2051	0.8204
5	0.2461	1.2305
6	0.2051	1.2306
7	0.1172	0.8204
8	0.0439	0.3512
9	0.0098	0.0882
10	0.0010	0.01
	Sum=	5.0005

Hence $\mu_{x}=\sum [x*P(x)]=5.00$

also using formula

$\sigma_{X}=\sqrt{\sum [X^{2}*P(X)]-\mu_{X}^{2}}$

$\sigma_{X}=\sqrt{27.5041 -25}=1.58$

(c) Again using formula

$\mu_{X}=n*p=10*0.5=5$

and $\sigma_{X}=\sqrt{n*P(1-P)}=1.58$

d) Probability distribution graph

The Binomial distribution is symmetric