Suppose Z is a standard normal random variable 1 If Pz Z z

Suppose Z is a standard normal random variable.

1. If P(-z < Z < z) = 0.06424, find z.

2. Find P(-1.72 < Z < -0.16).

**Carry all decimals until you reach your answer, then round to four decimals.**

Solution

1.

This is the middle area between -z and z. By symmetry, (1-0.06424)/2 = 0.46788 lie to the left of -z.

Thus a table or technology, we find that

-z = -0.080600083

Thus,

z = 0.080600083 [ANSWER]

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2.

z1 = lower z score =    -1.72      
z2 = upper z score =     -0.16      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.042716221      
P(z < z2) =    0.436440537      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.393724316   [ANSWER]