Question

Let X be normally distributed with mean μ = 18 and standard deviation σ = 14. [You may find it useful to reference the z table.]

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

b. Find P(X > 11). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

c. Find P(4 ≤ X ≤ 18). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

d. Find P(18 ≤ X ≤ 25). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

Solution :

a.

P(x 4)

= P[(x - ) / (4 - 18) / 14]

= P(z -1)

= 0.1587

P(x 4) = 0.1587

b.

P(x > 11) = 1 - P(x < 11)

= 1 - P[(x - ) / < (11 - 18) / 14)

= 1 - P(z < -0.5)

= 1 - 0.3085

= 0.6915

P(x > 11) = 0.6915

c.

= P[(4 - 18 / 14) (x - ) / (18 - 18 / 14) ]

= P(-1 z 0)

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

= 0.5 - 0.1587

= 0.3413

P(4 x 18) = 0.3413

d.

= P[(18 - 18 / 14) (x - ) / (25 - 18 / 14) ]

= P(0 z 0.5)

= P(z 0.5) - P(z 0)

= 0.6915 - 0.5

= 0.1915

P(18 x 25) = 0.1915