can someone explain how to get the percentage?

Question

The scores of adults on an IQ test are approximately Normal with mean 110 and standard deviation 17. An organization requires an IQ score of 144 or higher for membership. What percent of adults would qualify for membership? (Enter your answer to one decimal place.)

Answer 1

Note that 144 is two standard deviations above the mean. From a cumulative standard normal table, this corresponds to a z value of 2, (144-110)/17

 

The probability of being lower than 144 is 0.9772, from the standard normal table. The probability of being greater than 144 is 1-.9772 or 0.0228 or 2.28% of adults would qualify.

Answer 2

Prob ( X>=144) = 1 - Prob( X <=144)  <--- property of normal bell curve

 

                      = 1 - Prob( z <=  (144-110)/17 )    <--- converts to z score

 

                      = 1 - Prob ( z <= 2 )

 

                      = 1 - 0.9772  <---- per the normal distribution table

 

                      = 0.0228  = 2.28%