A researcher develops a test for selecting intellectually gi

A researcher develops a test for selecting intellectually gifted children, with a ? of 56 and a ?_X of 8. (a) What percentage of children are expected to score below 60? (b) What percentage of scores will be above 54? (c) A gifted child is defined as being in the top 20%. What is the minimum test score needed to qualify as gifted?

Using the test in the question above,you measure 64 children, obtaining a X of 57.28. Slug says that because this X is so close to the ? of 56, this sample could hardly be considered gifted. (a) Perform the appropriate statistical procedure to determine whether he is correct. (b) In what percentage of the top scores is this sample mean?

Solution

?=56

?=8

a) P( x < 60 ) = P( (x-?)/? < (60-56)/8 ) = P( z < .5) = .6915 \'look up value on z chart\'

b) P( x > 54 ) = P( (x-?)/? < (54-56)/8 ) = P( z > .25) = .4013

c) P( z > b ) = .20 find the z value that has probability of 20% to the left of its value.

P( z > .84 ) = .20

z = (x-?)/? = (x-56)/8 = .84 solve for x

.84*8 + 56 = 62.72

minimum test score of 62.72