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an instructor gives a course grade of b to students who have total score on exams and homeworks between 800 and 900, where the maximum possible is 1000. if the total scores have approximately a normal distribution with mean 830 and standard deviation 50, about what proportion of the students receive a b?



Answer :

Let x denote the score. Assuming x follows normal distribution with

mean m = 70 and SD = 5 ,

we first calculate P( x < or = 80)

The SNV is z = (x — m) /SD

When x = 80, Z = ( 80 — 70)/5 = 2

So, P( x < or= 80)

  • = P( z < or= 2)
  • = Area under the standard normal curve on LHS of z = 2
  • =0.5000 + 0.4772
  • =0. 9772, which is the relative frequency of x < or = 80

Given that total number of students is

  • N = 1000. Let f be the number of students who have scored < or equal to 80,
  • Then f/N = relative frequency = 0.9772
  • Hence f = 0.9772 X N = 0.9772 X 1000 = 977

learn more about binomial distrubution click here:

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