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 .

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:

Given that,

mean = = 547

standard deviation = = 100

a ) p ( x > 647)

= 1 - p (x < 647 )

= 1 - p ( x -  / ) < ( 647 - 547 /100)

= 1 - p ( z < -100 / 100)

= 1 - p ( z < 1 )

Using z table

= 1 - 0.8413

= 0.1587

Probability = 0.1587

GMAT scores is = 15.87%

b ) p ( x > 747)

= 1 - p (x < 747 )

= 1 - p ( x -  / ) < ( 747 - 547 /100)

= 1 - p ( z < 200 / 100)

= 1 - p ( z < 2 )

Using z table

= 1 - 0.9772

= 0.0228

Probability = 0.0228

GMAT scores is = 2.3%

c ) p ( 447 < x < 547 )

= p (447 - 547 / 100) < ( x -  / ) < ( 547 - 547 / 100)

= p ( - 100 / 100 < z < 0 / 100 )

= p (- 1 < z < 0 )

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

Using z table

= 0.5000 - 0.1587

= 0.3413

Probability = 0.3413

GMAT scores is = 34.13%

d ) p ( 347 < x < 647 )

= p (347 - 547 / 100) < ( x -  / ) < ( 647 - 547 / 100)

= p ( - 200 / 100 < z < 100 / 100 )

= p (- 2 < z < 1 )

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

Using z table

= 0.8413 -0.0228

= 0.8185

Probability = 0.8185

GMAT scores is = 81.9%