A stationary store has decided to accept a large shipment of ball-point pens if

Question

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 17 randomly selected pens yields no more than two defective pens.

(a) Find the probability that this shipment is accepted if 5% of the total shipment is defective. (Use 3 decimal places.)

(b) Find the probability that this shipment is not accepted if 20% of the total shipment is defective. (Use 3 decimal places.)

According to Harper's Index, 45% of all federal inmates are serving time for drug dealing. A random sample of 17 federal inmates is selected.

(a) What is the probability that 10 or more are serving time for drug dealing? (Use 3 decimal places.)

(b) What is the probability that 6 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.)

Explanation / Answer

a) No of defectives X here is Binomial with p = 0.05 and n =17

q = 1-p = 0.95

P(X=r) = 17C4 (0.05)r(0.95)17-r

P(X<=2) = P(X=0 or 1 or 2)

=0.950

b) P(X>2) when p = 0.2

= 0.690

n = 17 and p =0.45

Y no of federal inmates serving for drug dealing

a)P(x>=10) = 0.183

b) P(X<=6) =0.290

c) E(Y) = np = 17(0.45) = 7.65

=7.7

c)

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