I just need to make sure I got all of these right... For a normal distribution,
ID: 3171587 • Letter: I
Question
I just need to make sure I got all of these right...
For a normal distribution, the z-score location that would separate the distribution into two sections so that there is ...
a) 10% in the tail on the right-hand side is ____. (i got 1.2800)
b) 20% in the tail on the left-hand side is ____. (i got -0.8400)
c) 70% in the body on the right-hand side is ____. (i got -0.5200)
d) 75% in the body on the left-hand side is ____. (i got 0.67000)
(Make sure that you take your answer to two decimal places.)
- Thanks!
Explanation / Answer
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P ( Z > x ) = 0.1
Value of z to the cumulative probability of 0.1 from normal table is 1.2816
P( x-u/ (s.d) > x - 0/1) = 0.1
That is, ( x - 0/1) = 1.2816
--> x = 1.2816 * 1+0 = 1.28
b.
P ( Z < x ) = 0.2
Value of z to the cumulative probability of 0.2 from normal table is -0.842
P( x-u/s.d < x - 0/1 ) = 0.2
That is, ( x - 0/1 ) = -0.84
--> x = -0.84 * 1 + 0 = -0.84
c.
P ( Z > x ) = 0.7
Value of z to the cumulative probability of 0.7 from normal table is -0.5244
P( x-u/ (s.d) > x - 0/1) = 0.7
That is, ( x - 0/1) = -0.5244
--> x = -0.5244 * 1+0 = -0.52
d.
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 = 0.67