Question

The Graduate Management Admissions Test (GMAT) has a mean of 500 and a standard deviation of 100.  Using this information, find the probability for the three scenarios shown below.  (3.5 pts.)

Note: Show your z score rounded to two decimal places (i.e., 2.85) (Showing calculations may help you earn partial credit.) Show your probability rounded to four decimal places (i.e., .6560).

a) What is the probability of a GMAT score less than 548?    

b) What is the probability of a GMAT score being greater than 748?  

c) What is the probability of a GMAT score being between 548 and 748?

Answer 1

Solution :

Given that ,

mean = = 500

standard deviation = = 100

a) P(x < 548) = P[(x - ) / < (548 - 500) / 100 ]

= P(z < 0.48)

Using z table,

= 0.6844

b) P(x > 748) = 1 - p( x< 748)

=1- p P[(x - ) / < (748 - 500) / 100 ]

=1- P(z < 2.48)

Using z table,

= 1 - 0.9934

= 0.0066

c) P(548 < x < 748) = P[(548 - 500)/ 100) < (x - ) /  < (748 - 500) / 100) ]

= P(0.48 < z < 2.48)

= P(z < 2.48) - P(z < 0.48 )

Using z table,

= 0.9934 - 0.6844

= 0.3090