SOLUTION: Let X be normally distributed with mean μ = 142 and standard deviation σ = 28. [You may find it useful to reference the z table.] a. Find P(X ≤ 100). (Round "z" value to 2

Algebra ->  Probability-and-statistics -> SOLUTION: Let X be normally distributed with mean μ = 142 and standard deviation σ = 28. [You may find it useful to reference the z table.] a. Find P(X ≤ 100). (Round "z" value to 2      Log On


   

Question 1162651: Let X be normally distributed with mean μ = 142 and standard deviation σ = 28. [You may find it useful to reference the z table.]

a. Find P(X ≤ 100). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)


b. Find P(95 ≤ X ≤ 110). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)


c. Find x such that P(X ≤ x) = 0.400. (Round "z" value and final answer to 3 decimal places.)


d. Find x such that P(X > x) = 0.800. (Round "z" value and final answer to 3 decimal places.)


Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
=(100-142)/28=-1.5
prob z< -1.5 is 0.0668
z is -47/28 to -32/28
or -1.68 to -1.14
probability is 0.0807
inv norm for 0.400 is z=-0.253
-0.253=(x-142)/28
-7.084=x-142
x=134.916
z=0.842
0.842=(x-142)/28
x=165.576