Question

1. If X  is a normal distributed random variable with population mean 5 and population variance 4 , the probability that X  is lies between 1 and 7 is closest or equal to

0.0228

0.8185

0.1815

0.8413

2. Suppose X1  and X2  are both normally distributed random variables with population mean 10 and population variance 4. If X1  and X2   are independent, the probability that average of X1  and X2  lies between 8 and 12 is closest or equal to X2

0.9214

0.0786

0.1572

0.8428

3. A mortgage holding company has found that 0.1 of its mortgage holders default on their mortgage and lose the property. Furthermore, 0.85 of those who default are late on at least two monthly payments over the life of their mortgage as compared to 0.31 of those who do not default. What is the joint probability that a mortgagee has two or more late monthly payments and does not default on the mortgage?

0.765

0.085

0.031

0.279

Answer 1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	5
std deviation   =σ=	2.000

probability =

P(1<X<7)

=

P(-2<Z<1)=

0.8413-0.0228=

0.8185

2)

sample size       =n=	2
std error=σx̅=σ/√n=	1.4142

probability =

P(8<X<12)

=

P(-1.41<Z<1.41)=

0.9214-0.0786=

0.8427

3)

joint probability that a mortgagee has two or more late monthly payments and does not default on the mortgage =(1-0.1)*0.31 =0.279