Question

Suppose time taken to grade an exam-paper by an examiner has mean 12.8 min. and standard deviation 5 min. If the examiner has to grade 46 exam-papers, what is the approximate probability that she will finish grading in less than 609 min. (assuming grading times are independent and she grades continuously)? Answer to 4 decimal place

Answer 1

$\sum$ X ~ N( n $\mu$ , n $\sigma$ ² ) = (46 * 12.8 , 46 * 5² ) = (588.8 , 1150)

Using central limit theorem ,

($\sum$ X < x) = P(Z < x -  $\mu$ / sqrt (n $\sigma$ ² ) ) )

So,

P($\sum$ X < 609= sqrt ( P(Z < 609 - 588.8 / sqrt(1150) )

= P(Z < 0.60)

= 0.7257