Question

The average time it takes a group of students to complete a certain assignment is 36 minutes. The standard deviation is 4 minutes. Assume the variable is normally distributed. Now find the probability that if a group of 9 randomly selected students complete the assignment, the mean time it takes the group will complete the assignment in less than 33 minutes. Include drawings in your work. Use Traditional Method for hypothesis testing unless specified otherwise. Use correct rounding rule for final results!

Answer 1

X ~ N ( µ = 36 , σ = 4 )
P ( X < 33 )
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 33 - 36 ) / ( 4 / √9 )
Z = -2.25
P ( ( X - µ ) / ( σ/√(n)) = ( 33 - 36 ) / ( 4 / √(9) )
P ( X < 33 ) = P ( Z < -2.25 )
P ( X̅ < 33 ) = 0.0122 (From Z table)