Answer:
To be able to approximate the sampling distribution with a normal model, it is needed that and
, and both conditions are satisfied in this problem.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they will make payments on time, or they won't. The probability of a person making the payment on time is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The sampling distribution can be approximated to a normal model if:
and
Based on past experience, a bank believes that 8.9 % of the people who receive loans will not make payments on time.
This means that
The bank has recently approved 220 loans.
This means that
What must be true to be able to approximate the sampling distribution with a normal model?
To be able to approximate the sampling distribution with a normal model, it is needed that and
, and both conditions are satisfied in this problem.