Question

A variable is normally distributed with mean 7 and standard deviation 2.

a. Find the percentage of all possible values of the variable that lie between 2 and 8.

b. Find the percentage of all possible values of the variable that are at least 3.

c. Find the percentage of all possible values of the variable that are at most 5.

Answer 1

Solution :

Given that ,

mean = = 7

standard deviation = =2

P(2< x < 8) = P[(2 -7) /2 < (x - ) / < (8-7) / 2)]

= P(-2.5 < Z < 0.5)

= P(Z <0.5 ) - P(Z < -2.5)

Using z table   

= 0.6915 - 0.0062

=0.6853

=68.53%  

b.

Given that ,

mean = = 7

standard deviation = =2

P(x >3 ) = 1 - P(x<3 )

= 1 - P[(x -) / < (3- 7) /2 ]

= 1 - P(z < -2)

Using z table

= 1 - 0.9772

=0.0228

=2.28%

c.

P(x5 )

= 1 - P[(x -) / (5- 7) /2 ]

= 1 - P(z -1)

Using z table

= 1 - 0.1587

=0.8413

=84.13%