Shelias measured glucose level one hour after ingesting a su

Shelia\'s measured glucose level one hour after ingesting a sugary drink varies according to the Normal distribution with
= 126 mg/dl
and
= 13 mg/dl.
Let\'s consider what could happen if we took 4 separate measurements from Shelia. What is the blood glucose level L such that the probability is only 0.05 that the average of 4 measurements is larger than L? (Hint: This requires a backward Normal calculation. Round your answer to two decimal places.)

Solution

Normal Distribution
Mean ( u ) =126
Standard Deviation ( sd )= 13
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P ( Z < x ) = 0.95
Value of z to the cumulative probability of 0.95 from normal table is 1.645
P( x-u/s.d < x - 126/13/Sqrt(4) ) = 0.95
That is, ( x - 126/6.5 ) = 1.64
--> x = 1.64 * 6.5 + 126 = 136.6925