(a)
To find P(X23):
Applying Continuity Correction:
P(X>22.5):
Z = (22.5 - 20)/4
= 0.625
Table gives area= 0.2357
So,
P(X23) = 0.5 - 0.2357 = 0.2643
So,
Answer is:
0.2643
(b)
To find P(18X23):
Applying Continuity Correction:
To find P(17.5 < X < 23.5):
Case 1: For X from 17.5 to mid value:
Z = (17.5 - 20)/4
= - 0.625
Table gives area= 0.2357
Case 2: For X from mid value to 23.5:
Z = (23.5 - 20)/4
= 0.875
Table gives area= 0.3106
So,
P(18X23):= 0.2357 +0.3106 = 0.5463
So,
Answer is:
0.5463
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