# How to calculate z-Score

#### rubberduck

##### New Member
Hello
I have huge problem cause i have a test on tuesday and don't know anything about z-scores.
Here is the question:
Agricultural scientists are working on developing an improved variety of roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of roma plants produces fruit average of 74 grams, but 11% of the tomatoes are too small. It is reasonable to assume that a normal model applies.
a) what is the standad deviation of the weights of the Roams now being grown.
b)Scientists hope to reduce the frequency of undersized tomatoes to no more than 4% one way to accomplish this is the raise the average size of the fruit. ifthe standard deviation remains the same what target mean should they have as a goal?

The only thing i know is that i have to use that formula: z= (y-µ)/standard deviation. If there is a possiblity to do it on Minitab than pls tell me111

PLEASE GUYS HELP ME!!
Greets
RubberDuck

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#### JohnM

##### TS Contributor
You don't need Minitab to compute a z score. All you need is a calculator and the normal distribution table in your textbook.

z = (x - mu) / s

(1)

you're given mu = 74
you're also given that 11% of them are below 70, so x = 70

In your normal distribution table, if you look up the z score that marks the difference between the lower 11% and upper 89%, you should get -1.227

So, you now have:

-1.227 = (70 - 74) / s

Solve for s.

(2)

For this problem, keep s from problem (1).
You're told that they want to reduce the % below 70, so then the average must increase.

Find the z score that separates the lower 4% from the upper 96% - you should get -1.751.

-1.751 = (70 - mu) / s

Since you know s from problem (1), plug it in to this formula and solve for mu.

#### rubberduck

##### New Member
I have one more question cause i am just sitting in front of my book and looking at the normal distribution table but i can only find -1.23 and not -1.227. How did you get that?How did u calculate that?
thanks for ur helf man..i really appreciate that!!!!
Greetz
RubberDuck
I found a page that helped me..if there is some else who as stupid as i am u can't him the link: Still tell me how u calculated -1.227

http://www.oswego.edu/~srp/stats/z.htm

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#### JohnM

##### TS Contributor
I used the Excel function "=NORMSINV(0.11)"