Statistics Question (Find the z value corresponding to each of the following)

Question

Find the z value corresponding to each of the following:

a) Area to the right of the z value is 0.2743

b) Area to the left of the z value is 0.9965

c) Area to the right of z and to the left of 2.40 is 0.7176

Answer 1

You will need a Z table

a)  If the area to right of the z-value is ,2743 then the area to the left of the z value will be .7257

      and we see from the table z is .6.

b)  Area to the left of the z value is .9965 then from the table the z value is 2.7

c)  Area to to the right of z and to the left of 2.40 is .7176

     From the table we know that the area to the left of 2.40 is .9918 so we know the area greater than 2.4

     must be 1.0-.9918 = .0082 and the area between 0 and 2.4 must be .5000-.0082 = .4918 so we are looking for

     a z value ( a negative z) whose area to the left of z will be the difference ..9918 and .7176 (the area to the left of

     z)  That difference or area is .2743.  From the table we see z is -0.6 

 

      To check we know the area between -.6 and

      0 is .5000- .2743 = .2257 and the area between 0 and 2.4 is .9918-.5000 = .4918 and so the area between

      z = -0.6 and 2.4 is simply .2257 + .4918  =  .7175 which checks

 

I'd be delighted to tutor you online.  Regards, Terry