Question

Given that the data below was randomly selected from a lognormal distribution. What is the probability of the average of 39 randomly selected items being greater than 22.1? The data below is the complete SAMPLED data set. WE TOOK A SAMPLE FROM THE TOTAL POPULATION. YOU DO NOT GET ANY MORE DATA POINTS. IF YOU DON'T KNOW HOW TO SOLVE THIS, MOVE ON.

The question screen shot and answer is below. (Answer is 0.9755422) Please show how to arrive at this.

File Edit Modules Status About Given that the data below was randomly selected from a lognormal distribution What is the probability of the average of 39 randomly selected items being greater than 22.1? New Q View A X Six Sigma Study Guide Continuous Distributions St i Response 0.9755422 Check Response OK Data 2.48 11.02 21.45 125.35 0.04 0,08 120.03

Answer 1

from minitab the descriptive statistics of this data is

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
x 7 0 40.1 21.5 57.0 0.0 0.1 11.0 120.0 125.3

since the population is lognormally distributrd

P(x> 22.1) =

P(z> 22.1-40,1 57/V39 -40.1

P(x> 22.1) =

-18 P(z9,127

P(x> 22.1) = =

P(z 1.97217)

P ( Z>−1.97127 )=P ( Z<1.97127 )=0.9755 (from z table )