Question

The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is

a) More than $1000 P(x >1000)= , Calcuator part =

Answer=

b) less than $1280 P(x < 1280)= , Calcuator part =

Answer =

c) Between $800 and $1150 P(800 < x < 1150)= , Calculator part =

Answer =

Answer 1

Solution :

a)

P(x > 1000) = 1 - P(x < 1000)

= 1 - P[(x - ) / < (1000 - 982) / 180)

= 1 - P(z < 0.1)

= 1 - 0.5398

= 0.4602

P(x > 1000) = 0.4602

b)

P(x < 1280) = P[(x - ) / < (1280 - 982) / 180]

= P(z < 1.6556)

= 0.9511

P(x < 1280) = 0.9511

c)

P(800 < x < 1150) = P[(800 - 982)/ 180) < (x - ) /  < (1150 - 982) / 180) ]

= P(-1.0111 < z < 0.9333)

= P(z < 0.9333) - P(z < -1.0111)

= 0.8247 - 0.156

= 0.6687

P(800 < x < 1150) = 0.6687