Question

(a) Find the area above 140 for a N ( 160 , 25 ) distribution. Round your answer to three decimal places. Area = (a) Find the area below 200 for a N ( 160 , 25 ) distribution. Round your answer to three decimal places. Area =

Answer 1

Solution :

Given that ,

mean = = 160

standard deviation = = 25

(a)

P(x > 140) = 1 - P(x < 140)

= 1 - P((x - ) / < (140 - 160) / 25)

= 1 - P(z < -0.8)

= 1 - 0.2119   

= 0.7881

P(x > 140) = 0.788

Area = 0.788

(b) P(x < 200) = P((x - ) / < (200 - 160) / 25)

= 1 - P(z < 1.6)

= 1 - 0.9452

= 0.0548

P(x < 200) = 0.055

Area = 0.055