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

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