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 250 loans. What is the probability that between 4% and 6% of these clients will not make timely payments?

Answer 1

Solution :

Given that ,

p = 0.07

1 - p = 0.93

n = 250

= p = 0.07

= (p*(1-p))/n =  (0.07*0.93)/250 = 0.01614

P(0.04 < <0.06 ) = P((0.04-0.07)/0.01614 ) < ( - ) /  < (0.06-0.07) /0.01614 ) )

= P(-1.859 < z < -0.620)

= P(z < -0.620) - P(z < -1.859)

= 0.2676 - 0.0315

= 0.2361

Probability = 0.2361

The probability that between 4% and 6% of these clients will not make timely payments is 0.2361