Question

A professor noticed that the grades in his course are normally distributed. He has also noticed that his morning classes average 73, with a standard deviation of 12 on their final exams. His afternoon classes average 77, with a standard deviation of 10.What is the probability that the mean grade of four randomly selected students from a morning class is greater than the average grade of four randomly selected students from an afternoon class?

Answer 1

Solution :

Given that,

mean = = 73

standard deviation = = 12

n = 4

=   = 73

= / n = 12 / 4 = 6

P( > 77) = 1 - P( < 77)

= 1 - P[( - ) / < (77 - 73) / 6]

= 1 - P(z < 0.67)

Using z table,    

= 1 - 0.7486

= 0.2514