Question

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100 . ***(Please do by hand with explanation, as I cannot use excel on exam, TY)*** a. What percentage of GMAT scores are 647 or higher? b. What percentage of GMAT scores are 747 or higher (to 1 decimal)? c. What percentage of GMAT scores are between 447 and 547 ? d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

Answer 1

Solution:

= 547

= 100

( a )

P( x 647 ) = P( z ( 647 - 547 ) / 100 )

= P( z 1 )

= 0.15

( b )

P( x 747 ) = P( z ( 747 - 547 ) / 100 )

= P( z 2 )

= 0.02

( c )

P( 447 < x < 547 ) = P( ( 447 - 547 ) / 100 < z < ( 547 - 547 ) / 100 )

= P( z < (547-547)/100) - P( z < (447 - 547) / 100 )

= P( z < 0 ) - P( z < -1 )

= 0.5 - 0.1587

= 0.34

( d )

P( 347 < x < 647 ) = P(  ( 347 - 547 ) / 100 < z < ( 647 - 547 ) / 100 )

= P( z < (647-547)/100) - P( z < (347 - 547) / 100 )

= P( z < 1 ) - P( z < -2 )

= 0.9772 - 0.8413

= 0.02