SOLUTION: Question for my stat practice exam I cannot figure this out Determine the value of z* such that satisfies the conditions below. (Round your answers to two decimal places.) (a) &#

Question 1100726: Question for my stat practice exam I cannot figure this out
Determine the value of z* such that satisfies the conditions below. (Round your answers to two decimal places.)
(a) −z* and z* separate the middle 96.6% of all z values from the most extreme 3.4%
z* =
I got 2.12 I do not know if that is correct or not.

(b) −z* and z* separate the middle 90% of all z values from the most extreme 10%
(c) −z* and z* separate the middle 97.8% of all z values from the most extreme 2.2%
(d) −z* and z* separate the middle 92% of all z values from the most extreme 8%
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the area in the middle is .966, then the area on the outside is 1 - .966 = .034.

this area is split between the right sige of the area in the middle and thel eft side of the area in the middle.

therefore you are looking for a z-score that has an area of .017 to the right of it and a z-score that has an area of .017 to the left of it.

since most tables only tell you that area to the leftof the z-score, then you are looking for the z-score with an area of.017 to the left of it and a z-score with an area of 1 - .017 = .983 to the left of it.

the z-score with an area of .017 to the left of it is -.212

the z-score with an area of .983 to the left of it is 2.12

looks like you got it right.

the area will be between z-scores of -2.12 and 2.12

here's a picture of that that looks like.

$$$

follow the same procedure for the others and you should be ok.

1 minus area in between equals area outside.

half of the area outside is on the left and half of the area is on the right.

your problem c would be solved as:

area in between is .978.

area outside is equal to 1 - .978 = .022

half of .022 = .011

area outside on the left = .011 and area outside on the right = .011.

you would look for z-score with an area to the left of it = .011

that z-score would be equal to -2.29

since the normal distribution table is symmetric about the mean, than the z-score with an area of .011 to the right of it should be 2.29.

check the table for a z-score with an area of .011 to the right of it.

you do this by finding the z-score with an area of 1 - .011 = .989 to the left of it.

the z-score table tells you that the score with an area of .989 to the left of it is equal to 2.29

here's a picture.

$$$

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