4:41 PM webassign.net AT&T; LTE Your last submission is used for your scone My N

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4:41 PM webassign.net AT&T; LTE Your last submission is used for your scone My N According to Harper's Index, 45% of all federal inmates are serving time for drug dealing. A random sample of 14 federal inmates is selected (a) What is the probability that 11 or more are serving time for drug dealing? (Use 3 decimal places (b) What is the probability that 2 or fewer are serving time for drug dealing? (Use 3 decimal places.) (c) What is the expected number of inmates serving time for drug dealing? (Use 1 decimal place.) Submit Answer > Home My Assignments

Explanation / Answer

X ~ Binomial(14,0.45)

Where n = 14 , p = 0.45

Binomial probability distribution is

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

a)

p( X >=11) = p( x =11) + p( x = 12) + p( x =13) + p( x =14)

= 14C11 0.4511 0.553 + 14C12 0.4512 0.552 + 14C13 0.4513 0.55 + 14C14 0.4514 0.550

= 0.0114

b)

p(X <=2) = p( X =0) + p( x =1) + p( x =2)

= 14C0 0.450 0.5514 + 14C1 0.451 0.5513 + 14C2 0.452 0.5512

= 0.0170

c)

E(X) = n * p

= 14 * 0.45

= 6.3

  

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