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

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) = 0.360. (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 data

Population mean

Population Standard daviation

a) we have to find

So we have

X=100

now Z score for this is

From the Standard probablity distribution table the probablity value for Z= - 0.09 is

b) Now we have to find

when X= 95

now Z score for this is

From the Standard probablity distribution table the probablity value for Z= - 0.23 is

and   when X= 110

now Z score for this is

From the Standard probablity distribution table the probablity value for Z= 0.20 is

c)here given that

From the standard probablity distribution table the respective Z value for this is

Z= -0.358

Now we know that

d)    here given that

From the standard probablity distribution table the respective Z value for this is

Z= 0.806

Now we know that