Question

A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of the applicants would you expect to have a score of 400 or above

Answer 1

Solution :

Given that ,

mean = $\mu$ = 460

standard deviation = $\sigma$ = 80

P(x $\geq$ 400) = 1 - P(x  $\leq$ 400)

= 1 - P[(x - $\mu$ ) / $\sigma$ $\leq$ (400 - 460) / 80]

= 1 -  P(z $\leq$ -0.75)   

= 1 - 0.2266

= 0.7734

Answer = 0.7734