Question

2. . Determine the value for x assuming that X is normally distributed with a mean of 15 and a standard deviation of 2.

(a) P(X < 11)

(b) P(X > 0)

(c) P(3 < X < 7)

(d) P(-2 < X < 9)

(e) P(2 < X < 8)

Answer 1

Solution :

Given that ,

mean = = 15

standard deviation = = 2   

(a)

P(X<11 ) = P[(X- ) / < (11 -15) /2 ]

= P(z <-2 )

Using z table

= 0.0228

probability=0.0228

(B)P(x >0 ) = 1 - P(x<0 )

= 1 - P[(x -) / < (0 -15) /2 ]

= 1 - P(z <-7.5 )

Using z table

= 1 - 0

= 1

probability= 1

(c)

P(3< x <7 ) = P[(3 - 15) /2 < (x - ) / < (7 -15) /2 )]

= P( -6< Z <-4 )

= P(Z < -4) - P(Z <-6 )

Using z table   

= 0-0

   probability= 0

(d)

P(-2< x <9) = P[(-2 - 15) /2 < (x - ) / < (9 -15) /2 )]

= P( -8.5< Z <-3 )

= P(Z < -3) - P(Z <-8.5)

Using z table   

= 0.0013-0

   probability= 0.0013

(e)

P(2< x <8) = P[(2 - 15) /2 < (x - ) / < (8 -15) /2 )]

= P( -6.5< Z <-3.5 )

= P(Z < -3.5) - P(Z <-6.5)

Using z table   

=0.0002-0

   probability= 0.0002