# Confusion w/a""Standard Normal Probabilities" prob.

#### stud40111

##### New member
HI everyone. This is my first time posting, though I'm a long-time lurker. I pray that someone will pity me and assist me in getting the answer to this problem. THe problem is italicized below.

According to www.umich.edu/~isa/incoming/housing.html, in 2007 the monthly rental rates for one bedroom apartments in Ann Arbor, Michigan had a mean of $700. Suppose those rental rates have approximately a normal distribution, with a standard deviation of$150. Using a table, calculator, or software that can give normal probabilities, find the approximate proportion of one-bedroom apartments for which the rental rate:

a) is at least $1000 a month b) is less than$500 a month.

c) is between $500 and$1000 a month.

MY ATTEMPT TO ANSWER THE QUESTION THUS FAR:

a. = .025 (at least that's what I got by using the empirical rule....am I right?)

as for b and c, I've tried using a table at the back of my book entitled "Standard Normal Probabilities", I'm not sure how to use it because the numbers I get just don't make any sense. For instance, somehow I got the numbers .0982 for "b" and .725 for "c" while working on this problem at Panera bread earlier today and I have no clue how I got those numbers and even when I got them earlier today I wasn't sure if they were right.

Could anyone give me some help? This is due in about 14 hours (2pm Easter Standard Time for the U.S.).

Any and all help would be most appreciated.

#### wjm11

##### Senior Member
According to www.umich.edu/~isa/incoming/housing.html, in 2007 the monthly rental rates for one bedroom apartments in Ann Arbor, Michigan had a mean of $700. Suppose those rental rates have approximately a normal distribution, with a standard deviation of$150. Using a table, calculator, or software that can give normal probabilities, find the approximate proportion of one-bedroom apartments for which the rental rate:

a) is at least $1000 a month b) is less than$500 a month.

c) is between $500 and$1000 a month.

MY ATTEMPT TO ANSWER THE QUESTION THUS FAR:

a. = .025 (at least that's what I got by using the empirical rule....am I right?)

as for b and c, I've tried using a table at the back of my book entitled "Standard Normal Probabilities", I'm not sure how to use it because the numbers I get just don't make any sense. For instance, somehow I got the numbers .0982 for "b" and .725 for "c" while working on this problem at Panera bread earlier today and I have no clue how I got those numbers and even when I got them earlier today I wasn't sure if they were right.
You need to calculate a z value then use it in the table.

The z value is just the number of standard deviations that a value lies away from the mean. So, subtract the mean from the value of interest, then divide by the sd:

Z = (500 – 700)/150 = -1.33

Now go to Table A and look under the z column to find –1.3, then move sideways along that row until you are under the .03 column. The answer is about .0918. This means 9.18% of the rents are less than \$500.

Note: your "empirical rule" is contained in this table. Track the values down so it makes sense to you.