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

the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean of the sampling distribution ( x ) = 36
standard Deviation ( sd )= 4/ Sqrt ( 9 ) =1.3333
sample size (n) = 9

the probability that the mean time it takes the group will complete the assignment in less than 33 minutes.
P(X < 33) = (33-36)/4/ Sqrt ( 9 )
= -3/1.3333= -2.25
= P ( Z <-2.25) From Standard NOrmal Table
= 0.0122