Question

Seventy-one percent of American adults have at least one credit card. A bank surveys 200 randomly selected American adults, and finds that 136 have at least one credit card.

a) Define the random variable, X.
b) State the distribution of X. Check the relevant criteria.
c) Calculate ?̂.
d) State the approximate distribution of ?̂. Check the relevant criteria.

Answer 1

a) Let X denotes the number of American adults who have at least one credit card in a random sample of 200 American adults.

b) X ~ Binomial( n = 200, p = 0.71)

Here,

• A fixed number of trials.
• Each trial is independent of the others.
• There are only two outcomes.
• The probability of each outcome remains constant from trial to trial.

The probability mass function of X is

c)

d) or