Question

The First National Mortgage Company has noted that 8% of its customers pay their mortgage payments after the due date Upload a file detailing all of the work needed to answer the questions. Assume the data is normally distributed. Given a random sample of 150 customers, calculate the mean of the sample. (1 point) Given a random sample of 150 customers, calculate the standard deviation of the sample. (l point) What is the probability that in a random sample of 150 customers less than 7 will be late on their payments? (2 points) What is the probability that in a random sample of 150 customers at least 10 will be late on their payments? (2 points) a. b. с. d.

Answer 1

a)

n=	150	p=	0.0800
here mean of distribution=μ=np=		12

b)

and standard deviation σ=sqrt(np(1-p))=

3.3226

c)

for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

P(less then 7 will be late) :

probability =

P(X<6.5)

=

P(Z<-1.66)=

0.0485

d)

P(at least 10 will be late):

probability =

P(X>9.5)

=

P(Z>-0.75)=

1-P(Z<-0.75)=

1-0.2266=

0.7734