Use a factor tree to find the prime factorization of 164

explanation:

the loan estimate encourages consumers to shop. since it is the lenders who are required to issue a standardized loan estimate in a specific time frame, this way consumers are provided an opportunity to compare lenders and their products. otherwise consumer wouldn't know the benefits offered by other lenders.  

if a loan originator does not provide a loan estimate within 3 business days of receiving a completed loan application, that lender is in violation. lenders are required to issue a loan estimate within 3 days of applying for a loan or within 7 days prior to closing. having a loan estimate has following information.

not having loan estimate won't give you an idea of money to be borrowed.

you get to know your interest rates.

you also get to know if your interest rate can or may vary.

not having a good faith estimate can keep you unaware of aforementioned points.

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.