(Solution) Math 399N Week 5: Interpreting Normal Distributions

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?


Mean u= 100

Standard deviations a= 15

Sample size n=3

Value X bar= 115


First, we need to find the standard deviation of the sample using formula

S x=a/sqrt(n)

S x=15/sqrt(3)


Now, we need to find z score of x bar, using formula Z= x bar – u/Sx

Z=(115-100)/(15/sqrt (3) ) =15/8.6605= 1.732 = 0.9581 (using standards distribution table)

P(x>=115) = P(Z> 1.732) 1-0.9582= 0.0418 or 4.18%


Therefore the probability of sample 3 with mean 115 is 0.04. According to (Larson,……Please click the Paypal icon below to purchase full solution for only $5