Question

For X~N(100, 20) -

40 is greater than or equal to__

60 is greater than or equal to__ of values.

80 is less than or equal to__ of values.

Answer 1

Solution:
Given in the question that X is normal random variable
Mean = 100
Standard Deviation = 20
Solution(a)
P(X<40)
Z = (40-100)/20 = -3
From Z table we can say that P(X<40) = 0.0013
So 40 is greater than or equal to 0.13% of values
Solution(b)
P(X<60)
Z = (60-100)/20 = -2
From Z table we can say that P(X<60) = 0.0228
So 60 is greater than or equal to 2.28% of values.
Solution(c)
P(X>80) = 1-P(X<=80)
Z = (80-100)/20 = -1
From Z table we found P(X>80) = 1-0.1587 = 0.8413
So 80 is less than or equal to 84.13% of values.