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# Normal Distributions?

X has a normal distribution with a mean of 80.0 and a standard deviation of 4.0

Find

A. P(x<78.0) B. P(75.0 < x < 85.0) C. P(x > 82.0)

Thanks

### 1 Answer

- Anonymous9 years agoFavorite Answer
First find the z-score.

z-score=(x-μ)/σ

Then look up the p-value on a z-table.

Z table: http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

(Keep in mind that a z table finds the probability of all values below the value you specified.)

[A] z-score=(78.0-80.0)/4

z= -0.50

P-value on z table= .3085

Answer: [.3085]

[B] Do the same thing for this one also. Find the p-value for each specific value (75.0 and 85.0) but in this case you must subtract the p-value of the 85.0 from the p-value of the 75.0 to find the p-value in between the two specified values.

[C] Find p-value then subtract from 1 to find the probability of a value being over 82.0.

(P-value means the same thing as probability.)

You're welcome! (:

Hope this helps!

Source(s): AP Statistics :D