"The mean value of houses on a street is \S125,000 with a standard deviation of \$5,000. The dataset has a mound shaped distribution.
(a) Estimate the percent of houses between \$120,000 and \$135,000.
(b) Estimate the percent of houses below \$115,000."
I was given this homework problem on my Statistics one homework and I don't know how to solve this. The book doesn't have any examples of this type of problem. Any assistance would be appreciated.
I doubt very much that your stats book doesn't have information on the areas/probabilities for different regions of a normal distribution curve from around $-3$ to $+3$ standard deviations in single standard deviation regions. Nevertheless..........
Part a. is the region between one standard deviation below and two standard deviations above the mean. This is the area of the region between a Z score from $-1$ to $+2$ stated as a percentage of one.
Part b. is the area of region to the left of two standard deviation below the mean. This is the area below a Z score of $-2$ stated as a percentage of one.
Your book should have a table of Z sores. If not, use the table in this link http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf
For part a. The percentage of homes in this price range is the area to the left of a z score of $+2.0$ minus the area to the left for a Z score of $-1.0$ multiplied by $100$.
For part b. its simply the area to the left of a z score of $-2$ so simply read off the value in the table and multiply it by $100$ to get the percentage of homes in this price bracket.