Question
In: Statistics and Probability
If you have X~N (80,10) A) Calculate P(X>95) B) P(85≤X≤90) ROUND TO 4 DECIMAL PLACES
If you have X~N (80,10) A) Calculate P(X>95) B) P(85≤X≤90) ROUND TO 4 DECIMAL PLACES
Solutions
Expert Solution
Solution :
Given that ,
mean = 
= 80
standard deviation = 
= 10
(A)
P(x > 95) = 1 - P(x < 95)
= 1 - P((x -
) /
< (95 - 80) / 10)
= 1 - P(z < 1.5)
= 1 - 0.9332
= 0.0668
Probability = 0.0668
(B)
P(85 
X
90) = P((85 - 80 / 10) 
(x - 
) / 
(90 - 80 / 10) )
= P(0.5
z
1)
= P(z
1) - P(z
0.5)
= 0.8413 - 0.6915
= 0.1498
Probability = 0.1498
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