Question

Let X be normally distributed with mean μ = 20 and standard deviation σ = 12. [You may find it useful to reference the z table.]

a. Find P(X ≤ 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

b. Find P(X > 5). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

c. Find P(5 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

d. Find P(8 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

Solution :

a.

P(x 2)

= P[(x - ) / (2 - 20) / 12]

= P(z -1.5)

= 0.0668

P(x 2) = 0.0668

b.

P(x > 5) = 1 - P(x < 5)

= 1 - P[(x - ) / < (5 - 20) / 12)

= 1 - P(z < -1.25)

= 1 - 0.1056

= 0.8944

P(x > 5) = 0.8944

c.

= P[( 5 - 20/ 12) (x - ) / (20 - 20 / 12) ]

= P(-1.25 z 0)

= P(z 0) - P(z -1.25)

= 0.5 - 0.1056

= 0.3944

P(5 x 20) = 0.3944

d.

= P[(8 - 20 / 12) (x - ) / ( 20 - 20 / 12) ]

= P( -1 z 0)

= P(z 0) - P(z -1)

= 0.5 - 0.1587

= 0.3413

P(8 x 20) = 0.3413