Question

A standardized test was given to 6000 students. The scores were normally distributed with a mean of 380 and a standard deviation of 50. How many students scored between 280 and 380?

Answer 1

Solution =

Given, X follows Normal distribution with,

   = 380

   = 50

Find P( 280 < x< 380 )

= P(X < 380 ) - P(X < 280)

=  P[(X - )/ <  (380 - 380)/50] -   P[(X - )/ <  (280 - 380)/50]

= P[Z < 0.00] - P[Z < -2.00]

= 0.5 - 0.0228   ..Use z table

= 0.4772

Answer : P( 280 < x< 380 ) = 0.4772