Question

Given that 1% of the population are left handed, if a random sample of 1000 people is selected where x denotes the number of left handed people,

a) The random variable X is (choose one)

i) Binomial

ii) hypergeometric

iii) Poisson

iv) Normal

v) Exponential

vi) Uniform

b) Give the expectation value and variance of X.

c) Find the probabilities P(X=6) and P(X≥6).

d) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X, since the probability of success is small (rare)?

Answer 1

(d) since probability of success is too small,

therefore, we can use

Poisson approximation to binomial to the distribution of X.