Question

The entire home mortgage process has several parts, including getting pre-approved, getting the home appraised, and...

The entire home mortgage process has several parts, including getting pre-approved, getting the home appraised, and getting the actual loan. According to a study conducted by Realtor.com, in a normal market, this process takes 30 days on average, with a standard deviation of 5.75 days. The number of days to complete the entire home mortgage process is normally distributed.

a)The probability that a single mortgage loan selected at random will take less than 27 days to process is ______

b) The probability that a single mortgage loan selected at random will take more than 25 days to process is ______

(Report your answer as a percentage to 4 decimal places, using conventional rounding rules)

c) What percent of the mortgage loans will take between 28 and 33 days to process? ______ %

d) Seventy-three percent of the mortgage loans should take less than how many days to process? ______ days.

solution:-

given that mean = 30 , standard deviation = 5.75

formula z = (x-mean)/standard deviation

a) P(x < 27)

=> P(z < (27-30)/5.75)

=> P(z < -0.52)

=> 1 - P(z < 0.52)

=> 1 - 0.6985

=> 0.3015

b) P(x > 25)

=> P(z > (25-30)/5.75)

=> P(z > -0.87)

=> P(z < 0.87)

=> 0.8078

c) P(28 < X < 33)

=> P((28-30)/5.75 < z < (33-30)/5.75)

=> P(-0.35 < z < 0.52)

=> P(z < 0.52) - P(z < -0.35)

=> P(z < 0.52) - (1 - P(z < z < 0.35))

=> 0.6985 - (1-0.6368)

=> 0.3353

=> 33.53

d) Seventy-three percent of the mortgage loans should take less than how many days to process

the z value corresponding to the probability of 0.73 from standard normal table

z = 0.613

formula

=> x = z*standard deviation + mean

=> x = 0.613*5.75 + 30

=> x = 33.5248

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