Find the value of z if the area under a standard normal curve a. to the right of z is 0.3622 b. to the left of z is 0.1131 c. between 0 and z, with z > 0, is 0.4838 d. between —z and z, with z > 0, is 0.950
Answers
Given : area under a standard normal curve
a. to the right of z is 0.3622
b. to the left of z is 0.1131
c. between 0 and z, with z > 0, is 0.4838
d. between —z and z, with z > 0, is 0.950
To Find : value of z in each case
Solution:
Area under standard normal curve is 1
Area both side of z = 0 is 0.5
Area under a standard normal curve to the right of z is 0.3622
=> area to the left of z is 1- 0.3622 = 0.6378
From z score table :
z score Area to the left
0.35 ≈ 0.6368
0.36 ≈ 0.6406
Hence z score for 0.6378 is about 0.352
left of z is 0.1131
-2.28 represent 0.113
Hence z about -2.28 area on left 0.1131
c. between 0 and z, with z > 0, is 0.4838
z = 0 represent 0.5
between 0 and z is 0.4838
Hence on left of z is 0.9838
z = 2.14
d. between —z and z, with z > 0, is 0.950
0.950 Hence between 0 to - z and 0 to z
is 0.950 /2 = 0.475
Left of -z = 0.5 - 0.475 = 0.025
left of z = 0.5 + 0.475 = 0.975
z = 1.96
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