Answer the following questions using the standard normal dis

Answer the following questions using the standard normal distribution:

A) Write the values of the following about the standard normal distribution:

mean __________________

standard deviation _______________

B) What is the probability that a z-score is between -1.2 and 1.74? _________________

C) What percent of data is more than z=1.56? _________________________

D) What z-score represents the 45^th percentile? _______________________

E) What is the value of Z_0.75? ______________________________

F) What is the total area under the standard normal distribution curve? _____________

Solution

Normal Distribution
a)
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -1.2) = (-1.2-0)/1
= -1.2/1 = -1.2
= P ( Z <-1.2) From Standard Normal Table
= 0.11507
P(X < 1.74) = (1.74-0)/1
= 1.74/1 = 1.74
= P ( Z <1.74) From Standard Normal Table
= 0.95907
P(-1.2 < X < 1.74) = 0.95907-0.11507 = 0.844                  
c)
P(X > 1.56) = (1.56-0)/1
= 1.56/1 = 1.56
= P ( Z >1.56) From Standard Normal Table
= 0.0594                  
d)
P ( Z < x ) = 0.45
Value of z to the cumulative probability of 0.45 from normal table is -0.126
P( x-u/s.d < x - 0/1 ) = 0.45
That is, ( x - 0/1 ) = -0.13
--> x = -0.13 * 1 + 0 = -0.126                  
e)
P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 0/1 ) = 0.75
That is, ( x - 0/1 ) = 0.67
--> x = 0.67 * 1 + 0 = 0.674