Question

In a shipment of 20,000 toys (called robot chickens) 600 of the toys are defective. Suppose that 20 toys are selected at random (without replacement) for inspection, and let X denote the number of defective toys found.

a) The distribution of the random variable X is (choose one)

i) Binomial

ii) hypergeometric

iii) Poisson

iv) Normal

v) Exponential

vi) Uniform

b) Find P(X≤6).

c) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X if we assume they are selected with replacement? With this approximation find P(X≤6).

d) If we make the assumption that they are selected with replacement as in part (c), since 600/20,000=0.03 is small (hint - rare) and since we have select enough components (hint – large n) the distribution in (c) can be approximated by which distribution listed in (a) ? With this approximation find P(X≤6)

Answer 1