SOLUTION: Suppose Z is a standard normal random variable. If P(-z < Z < z) = 0.5588, find z. Find P( -2.46 < Z < -0.16). Please help me out! Thank you so much

Question 1069362: Suppose Z is a standard normal random variable.
If P(-z < Z < z) = 0.5588, find z.
Find P( -2.46 < Z < -0.16).
Please help me out!
Thank you so much
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
While you can use the table, and it is worth learning, the calculator can be used, too.
2nd VARS 2 normal cdf
-2.46,-0.16 ENTER
0.4295. This makes sense, because it is almost half of the curve from -3 to 0.
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For -z This is centered on z=0
half of this is 0.2794
Therefore, from the table, you want where z is 0.5+/- 0.2794, or where the prob is 0.2206 and 0.7794
this is at 0.77 and -0.77. Find the four digit probability in the middle of the table and look to the left margin for the unit or tenth of a unit. The top margin will be the hundredths of a unit. Most of the time, a z to the nearest hundredth is what is desired. This should be symmetrical, and it is.

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