Question

Let X be normally distributed with mean μ = 103 and standard deviation σ = 35. [You may find it useful to reference the z table.]

c. Find x such that P(X ≤ x) = 0.360. (Round "z" value and final answer to 3 decimal places.)

d. Find x such that P(X > x) = 0.790. (Round "z" value and final answer to 3 decimal places.)

Answer 1

Given that,

mean = = 103

standard deviation = = 35

Using standard normal table,

P(Z < z) = 0.360

= P(Z < z) = 0.360  

= P(Z < -0.36) = 0.360

z = -0.36 Using standard normal z table,

Using z-score formula  

x= z * +

x= -0.36*35+103

x= 90.400

B.

P(Z > z) =0.790

= 1 - P(Z < z) = 0.790  

= P(Z < z) = 1 - 0.790

= P(Z < z ) = 0.21

= P(Z < -0.81) = 0.21

z =-0.81

Using z-score formula,

x = z * +

x = -0.81* 35+103

x = 74.650