Question

11) A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 312 and a standard deviation of 50.

What proportion of students taking the exam receive a score that is within 64 points of the mean?

Round your answer to 4 decimal places.

Answer 1

Solution:

Given, the Normal distribution with,

   = 312

= 50

P(within 64 points of the mean)

= P[312 - 64 < X < 312 + 64]

= P[248 < X < 376]

= P(X < 376) - P(X < 248)

=  P[(X - )/ <  (376 - 312)/50] -   P[(X - )/ <  (248 - 312)/50]

= P[Z < 1.28] - P[Z < -1.28]

= 0.8997 - 0.1003..Use z table

= 0.7994