rime the tollorwing yprab bi ki tis Pla La owm PIGL x 24 Sol

rime the tollorwing yprab bi ki tis Pla La owm PIGL x 24)

Solution

Normal Distribution
Mean ( u ) =25
Standard Deviation ( sd )=4
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 22) = (22-25)/4
= -3/4 = -0.75
= P ( Z <-0.75) From Standard Normal Table
= 0.22663
P(X < 26) = (26-25)/4
= 1/4 = 0.25
= P ( Z <0.25) From Standard Normal Table
= 0.59871
P(22 < X < 26) = 0.59871-0.22663 = 0.3721                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 19) = (19-25)/4
= -6/4 = -1.5
= P ( Z <-1.5) From Standard Normal Table
= 0.06681
P(X < 24) = (24-25)/4
= -1/4 = -0.25
= P ( Z <-0.25) From Standard Normal Table
= 0.40129
P(19 < X < 24) = 0.40129-0.06681 = 0.3345                  
c)
P(X > 23) = (23-25)/4
= -2/4 = -0.5
= P ( Z >-0.5) From Standard Normal Table
= 0.6915