Question

A budgeting Web site reported that 35​% of U.S. households have withdrawn money from a​ 401(k) or other retirement account for needs other than retirement in 2013. A random sample of 11 U.S. households was selected. Complete parts a through e below. a. What is the probability that exactly four households withdrew funds from a retirement account for needs other than​ retirement? The probability is . 2428. ​(Round to four decimal places as​ needed.) b. What is the probability that less than six households withdrew funds from a retirement account for needs other than​ retirement? The probability is . 8513. ​(Round to four decimal places as​ needed.) c. What is the probability that more than eight households withdrew funds from a retirement account for needs other than​ retirement? The probability is . 0020. ​(Round to four decimal places as​ needed.) d. What are the mean and standard deviation for this​ distribution? The mean for this distribution is nothing. ​(Type an integer or a​ decimal.)

Answer 1

Ans:

Use binomial distribution with n=11 and p=0.35

P(x=r)=11C_r*0.35^r*(1-0.35)^11-r

x	P(x)
0	0.0088
1	0.0518
2	0.1395
3	0.2254
4	0.2428
5	0.1830
6	0.0985
7	0.0379
8	0.0102
9	0.0018
10	0.0002
11	0.0000

a)P(x=4)=0.2428

b)P(x<6)=P(x<=5)

=P(x=0)+..............+P(x=5)

=0.0088+0.0518+0.1395+0.2254+0.2428+0.1830

=0.8513

c)P(x>8)=P(x=9)+P(x=10)+P(x=11)

=0.0018+0.0002+0.0000

=0.0020

d)mean=np=11*0.35=3.85

standard deviation=sqrt(npq)=sqrt(11*0.35*0.65)=1.5819