If Test X has a mean of 50, standard deviation of 10 (assuming a normal distribution), and N= 1000, about how many individuals score between 40 and 60?

Question

If Test X has a mean of 50, standard deviation of 10 (assuming a normal distribution), and N= 1000, about how many individuals score between 40 and 60?

If Test X has a mean of 50, standard deviation of 10 (assuming a normal distribution), and N= 1000, about how many individuals score between 40 and 60?

Answer 1

Prob ( 40 < X < 60) = 

 

Prob( (40-50)/10 < z < (60-50)/10 ) =

 

Prob ( -1 < z < 1) =

 

Prob ( z<1) - Prob ( z < -1)

 

 = .8413 - .1587

 

= .6826 = 68.26%

 

68.26% of 1000 = 682.6 of them will score between 40 and 60