Given this data set 3621234 aConvert each of these values to

Given this data set: 3,6,2,1,2,3,4

a)Convert each of these values to a z score

b) What percentage of cases would you expect to fall below 2?

c) what score would be at the 90^th percentile?

Given this data set: 2, 3, 3, 1, 4, 2, 3

a) Convert each of these values to a z score

b) What percentage of cases would you expect to fall below 3?

c) What score would be at the 40^th percentile?

Solution

Sample Mean = 3
Sample S.d = 1.633
n=7
a)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
X = 3 => Z = (3-3)/1.633
Z = 0/1.633= 0

X = 6 => Z = (6-3)/1.633
Z = 3/1.633= 1.8371

X = 2 => Z = (2-3)/1.633
Z = -1/1.633= -0.6124
                  

X = 1 => Z = (1-3)/1.633
Z = -2/1.633= -1.2247
                  
X = 4 => Z = (4-3)/1.633
Z = 1/1.633= 0.6124

b)
P(X < 2) = (2-3)/1.633
= -1/1.633= -0.6124
= P ( Z <-0.6124) From Standard Normal Table
= 0.2701                  
~ 27.01% are fall below 2

c)
P ( Z < x ) = 0.9
Value of z to the cumulative probability of 0.9 from normal table is 1.282
P( x-u/s.d < x - 3/1.633 ) = 0.9
That is, ( x - 3/1.633 ) = 1.28
--> x = 1.28 * 1.633 + 3 = 5.0935