X is a normally distributed random variable with mean 15 and

X is a normally distributed random variable with mean, =15 and variance, 2= 25. Using z-table, calculate the following probabilities.

a. P(x0).

b. P(x5).

c. P(x10)

d. P(x15)

e. P(x20)

f. P(x0)

g. P(x5)

h. P(x10)

i. P(x15)

j. P(x20)

Note: forget about the first one that i posted it didn\'t copy exactly the question. This one is the appropriate one. Thank you

Solution

a)
Normal Distribution
Mean ( u ) =15
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X <= 0) = (0-15)/5
= -15/5= -3
= P ( Z <-3) From Standard Normal Table
= 0.0013                  
b)
P(X <= 5) = (5-15)/5
= -10/5= -2
= P ( Z <-2) From Standard Normal Table
= 0.0228                  
c)
P(X <= 10) = (10-15)/5
= -5/5= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587                  
d)
P(X <= 15) = (15-15)/5
= 0/5= 0
= P ( Z <0) From Standard Normal Table
= 0.5