Question

4. The SC First Mortgage Company has noted that 6% of its customers pay their mortgage payments after the due date.
   

a.	What is the probability that in a random sample of 150 customers 7 will be late on their payments?
b.	What is the probability that in a random sample of 150 customers at least 10 will be late on their payments?

Answer 1

X ~ Bin(n,p)

Where n = 150 , p = 0.06

Mean = np = 150 * 0.06 = 9

Standard deviation = sqrt (np(1-p))

= sqrt ( 150 * 0.06 ( 1 - 0.06) )

= 2.9086

a)

Using normal approximation ,

P(X < x) = P(Z < ( x - Mean ) / SD)

So,

P(X = 7) = P( 6.5 < X < 7.5) (With continuity correction )

= P(X < 7.5) - P(X < 6.5)

= P(Z < (7.5 - 9) / 2.9086) - P(Z < (6.5 - 9) / 2.9086)

= P(Z < -0.52) - P(Z < -0.86)

= 0.3015 - 0.1949

= 0.1066

b)

P(X >= 10) = P(X > 9.5) (With continuity correction )

= P(Z > (9.5 - 9) / 2.9086)

= P(Z > 0.17)

= 0.4325