Maths statistic need help to resolve a problem

[emelinedls]

Hello,

 

I need to finish that for tonight and I dont know what to use and what to do. If anyone can help me that would be great.

 

The average base salary for a store manager (Wal-Mart) in Sacramento, is $68,000, and the average base salary for a store manager (Wal-Mart) in San Francisco,is $78,000. Assume that salaries are normally distributed, the standard deviation for store managers in Sacramento is $20,000, and the standard deviation for store managers in San Francisco is $22,000.

 

(A) What is the probability that a store manager in Sacramento has a base salary in excess of $100,000?

 

(B) What is the probability that a store manager in San Francisco has a base salary in excess of $100,000

 

© What is the probability that a store manager in San Francisco has a base salary of less than $67,000

 

(D) How much would a store manager in San Francisco have to make in order to have a higher salary than 98.21% of the store managers in Sacramento

 

(E) Based the results from (A)-(D), if you are a job applicant for store manager position (Wal-Mart) in California, how would you negotiate annual salary using at least 200 words.

[KipIngram]

Do you understand how to draw a bell curve given a mean and standard deviation? That's step one. Imagine that you have done so. Then for part a, for example, you find $100,000 on the curve for Sacramento, and you determine what fraction of the area of that curve lies to the right of the $100k mark on the x axis. You will have to use tables for this, because there's no closed-form integral for the bell curve function.

 

All of A-D use that same sort of reasoning, so let's see where that gets you. Post again if you have more questions.

[swansont]

You have to show what you've done and how you think you should be answering. What's the equation that describes a normal distribution?

[emelinedls]

Do you understand how to draw a bell curve given a mean and standard deviation? That's step one. Imagine that you have done so. Then for part a, for example, you find $100,000 on the curve for Sacramento, and you determine what fraction of the area of that curve lies to the right of the $100k mark on the x axis. You will have to use tables for this, because there's no closed-form integral for the bell curve function.

 

All of A-D use that same sort of reasoning, so let's see where that gets you. Post again if you have more questions.

 

Thank you so much for your answer. I drew my bell curve. Then, I did not really understand what I have to do. Do I need to use p(x>100000) and to calculate z ?

You have to show what you've done and how you think you should be answering. What's the equation that describes a normal distribution?

I did a bell curve. I was going to use p(x>100000) by calculating z. Is it good if i do that ?

[KipIngram]

Yes, the tables I referred to are usually given as the probability of <= the value of X. So if you look up your mean value in the table you should get 0.5, which makes sense since half of the curve is to the left of that point and half to the right. As you look up higher and higher values the probability will grow, until it finally approaches 1.0 at the right side of the curve.

 

So if you've drawn it correctly then the area to the right of x=100000 is the area you want (probability of x > 100000), so you would take 1.0 minus the value given in the table.

This should help you understand why the standard deviation matters - if it is large then the curve "spreads out" further, and the probability of being above a specific x value will be lower. If standard deviation is lower, then the curve is "sharper, and the probability of being above that specific x will be lower.

[emelinedls]

Yes, the tables I referred to are usually given as the probability of <= the value of X. So if you look up your mean value in the table you should get 0.5, which makes sense since half of the curve is to the left of that point and half to the right. As you look up higher and higher values the probability will grow, until it finally approaches 1.0 at the right side of the curve.

 

So if you've drawn it correctly then the area to the right of x=100000 is the area you want (probability of x > 100000), so you would take 1.0 minus the value given in the table.

This should help you understand why the standard deviation matters - if it is large then the curve "spreads out" further, and the probability of being above a specific x value will be lower. If standard deviation is lower, then the curve is "sharper, and the probability of being above that specific x will be lower.

 

okay. So that should be μ=68000, σ=20000 ?

Then I found z=1.6.

I did p(z>1.6)=1-0.9452=0.0548

So that means only5.48% that a store manager in Sacramento has a salary in excess of $100,000?

 

If what I did it write i need to do the same for question B, C and D ?

[KipIngram]

I haven't checked your numbers against a table, but that seems reasonable, since 100000 is 100000 is 1.6 deviations above the mean; you'd expect a small percentage. And yes, the other problems all involve more or less the same procedure; you just have to choose the right city's mean and standard deviation. Be careful on part C, because you're asked for the probability that it's less than instead of greater than, so you don't do the subtraction from one. And for part D you're working backwards - working from a percentage to a salary. But it's the same general relationships in every case.

[emelinedls]

I haven't checked your numbers against a table, but that seems reasonable, since 100000 is 100000 is 1.6 deviations above the mean; you'd expect a small percentage. And yes, the other problems all involve more or less the same procedure; you just have to choose the right city's mean and standard deviation. Be careful on part C, because you're asked for the probability that it's less than instead of greater than, so you don't do the subtraction from one. And for part D you're working backwards - working from a percentage to a salary. But it's the same general relationships in every case.

 

thank you so much for your help I think I finished question A, B and C. However I did not understand what to do for question D. I have several calculations before t get to the result?

[KipIngram]

Yes. The only difference is that this time you are starting with the percentage. You draw your bell curve for the right city (I'm leaving it to you to decide which one - we're not supposed to give answers here; just help). Then instead of putting in a salary and figuring out a percentage, you start with the percentage and figure out the salary. Just precisely the reverse of the earlier problems. They're throwing you curve balls by mentioning both cities, but if you read it carefully you'll see what to do. One of the mentioned cities doesn't matter. Such tricks in problems are called "red herrings." They're designed to cause confusion if you don't have a full understanding, and so help them figure out which students do really understand and which ones don't.

[emelinedls]

Yes. The only difference is that this time you are starting with the percentage. You draw your bell curve for the right city (I'm leaving it to you to decide which one - we're not supposed to give answers here; just help). Then instead of putting in a salary and figuring out a percentage, you start with the percentage and figure out the salary. Just precisely the reverse of the earlier problems. They're throwing you curve balls by mentioning both cities, but if you read it carefully you'll see what to do. One of the mentioned cities doesn't matter. Such tricks in problems are called "red herrings." They're designed to cause confusion if you don't have a full understanding, and so help them figure out which students do really understand and which ones don't.

 

Okay thank you, so if i understood I use Sacramento. by using a table I found z=2.1 with 98.21%. I wanted to know if I was doing the right thing. Because I am still a little confused. Do I need to use this formula z=(x-μ) /σ ? or I need to use the formula with a p?

[KipIngram]

For part D you find your starting number (the percentage) in the table (i.e., from the part of the table your answers came from for earlier parts). Then you use the x value associated with that, which will be expressed as a number of standard deviations away from the mean. So you use your mean and standard deviation to convert that to dollars.

 

So yes, I think what you described is right. Tell me what your answer was (the salary required to be more than 98.21%. It will let me see if it "feels right."

I know you're focused on getting something finished right now, but if you'd like to PM questions to me from time to time I'd be glad to help you get a "core understanding" of this stuff. You can do an awful lot with even fairly simple statistics; it's a good skill to have.