Question

The average time it takes a group of young people to complete a The Children of Alcoholic Screening Test (CAST) is 48 minutes. The standard deviation is 7 minutes. Assume the variable is normally distributed. Find the probability that if 31 randomly selected youngsters complete the test, the mean time it takes the group to complete the test will be less than 28.4 minutes.

Answer 1

X ~ N ( µ = 48 , σ = 7 )
P ( X < 28.4 )
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 28.4 - 48 ) / ( 7 / √31 )
Z = -15.59
P ( ( X - µ ) / ( σ/√(n)) = ( 28.4 - 48 ) / ( 7 / √(31) )
P ( X < 28.4 ) = P ( Z < -15.59 )
P ( X̅ < 28.4 ) = 0