Question

Let X be normally distributed with mean μ = 17 and standard deviation σ = 8. [You may find it useful to reference the z table.]

a. Find P(X ≤ 1). (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(7 ≤ X ≤ 15). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

d. Find P(11 ≤ X ≤ 19). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

solution:-

a. Find P(X ≤ 1)

=> P(z ≤ (1-17)/8) = P(z < -2)

= 0.0228

b. P(X > 5) = P(z > (5-17)/8)

= P(z > -1.5)

= P(z < 1.5)

= 0.9332

c. Find P(7 ≤ X ≤ 15)

=> P((7-17)/8 < z < (15-17)/8)

=> P(-1.25 < z < -0.25)

=> P(z < -0.25) - P(z < -1.25)

= (1-P(z < 0.25)) - (1-P(z < 1.25))

= (1-0.5987) - (1-0.8944)

= 0.2957

d. P(11 ≤ X ≤ 19)

=> P((11-17)/8 < z < (19-17)/8)

=> P(-0.75 < z < 0.25)

=> P(z < 0.25) - P(z < -0.75)

=> P(z < 0.25) - (1-P(z < 0.75))

=> 0.5987 - (1-0.7734)

=> 0.3721