Question

According to Harper's Index, 40% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected.

(a) What is the probability that 11 or more are serving time for drug dealing? (Round your answer to three decimal places.)

(b) What is the probability that 5 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)

(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)

Answer 1

(a)

Binomial Distribution

n = 16

p = 0.4

q = 1- p = 0.6

P(X11) = P(X=11) + P(X=12) + P(X=13) + P(X=14) +P(X=15) + P(X = 16)

So,

P(X11)= 0.019

(b)

P(X5) = P(x=5) +P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)

So,

P(X5) = 0.329

(c)

Expected number = np = 16 X 0.4 = 6.4