k or other retren ent account for needs ut Abu geen Web site reported that 20% o

Question

k or other retren ent account for needs ut Abu geen Web site reported that 20% of US ious holds have withdrawn money from a 40 A randam samole of 11 U S housaholds was selected Complete parts a through e beiow man retrementa, 2013. a. What is the probalbiliy that exacly three households withdrew funds fiom a retirement account for ineeds ather Ihan retiremant? The probablity is 02215 Round to four decimal places as needed b. What is the probability that less than five househoids wiahdrew funds from a retirement account for needs otter than retirement? The probability is 0 9497 Round to four decimal places as needed) c. What is the probslbihy that more than six households withcrew. funds from a retiemant account for needs cenar tharn retreiment? The probability is 0 0020 Round to four decimal placas ss needed) d. What are the mean and standard deviation for this diatribution The mean for this distribution is Type an nteger ar a decimal.) Enter your answer in the answer box and then click Check Answer

Explanation / Answer

X ~ Binomial(11 , 0.20) , Where n = 11 and p = 0.20

Binomial probability distribution is

p(x) = nCx px (1-p)n-x

a)

p(x =3) = 11C3 0.203 0.808

= 0.2215

b)

p( x < 5) = p( x <=4)

= p( x =0) + p( x =1) + p( x =2) + p( x =3) + p( x =4)

= 11C0 0.200 0.8011 + 11C1 0.201 0.8010 + 11C2 0.202 0.809 + 11C3 0.203 0.808 + 11C4 0.204 0.807

= 0.9497

c)

p(x > 6) = p( x >= 7)

= p( x = 7) +p( x = 8) +p( x = 9) +p( x = 10) +p( x = 11)

= 11C7 0.207 0.804 + 11C8 0.208 0.803 + 11C9 0.209 0.802 + 11C10 0.2010 0.80 + 11C11 0.2011 0.800

= 0.0020

d)

Mean = np = 0.20 * 11 = 2.2

Standard deviation = Sqrt(np(1-p) )

= sqrt( 11 * 0.20 * 0.80)

= 1.3266

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