Question

Find the propability that x is between six and twelve.
X~N(8,2)

Round your answers to four decimal places.

Answer 1

Solution:

Given, the Normal distribution with,

   = 8

= 2

Find the probability that x is between six and twelve. i.e. P(6 < X < 12)

P(6 < X < 12)

= P(X < 12) - P(X < 6)

=  P[(X - )/ <  (12 - 8)/2] -   P[(X - )/ <  (6 - 8)/2]

= P[Z < 2.00] - P[Z < -1.00]

= 0.9772 - 0.1587   ..Use z table

= 0.8185

The probability that x is between six and twelve is  0.8185.

{To find P[Z < 2.00] , go to z table. See the column of z . See 2.0 in this table and see corresponding value in the row at .00 }