Based on past experience, a bank believes that 7% of the people who receive loan

Question

Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments? b) What is the distribution of clients in this group who may not make timely payments? c) What's the probability that over 10% of these clients will not make the payment?( This is a sampling distribution question because 200 people is a sample)

Explanation / Answer

a)mean proportion =0.07

std deviation =(p(1-p)/n)1/2 =0.018

b)as np>10 and n(1-p)>10 the distribution will be approximately normal

c)P(X>0.1) =1-P(X<0.1)=1-P(Z<0.1-0.07)/0.018)=1-P(Z<1.6628)=1-0.9518=0.0482

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