Question

Shelia's measured glucose level one hour after a sugary drink varies according to the normal distribution with u 124 mg/dl and σ-10.2 mg/dl. What is the level L such that there is probability only 0.01 that the mean glucose level of 4 test results falls above L? Give your answer precise to one decimal place

Answer 1

Solution :  

$\mu$_{$\bar x$} = 124

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 10.2 / $\sqrt$ 4 = 5.1

P(Z > 2.326) = 0.01

z = 2.326

$\bar x$ = z * $\sigma$ _{$\bar x$}+ $\mu$ _{$\bar x$} = 2.326 * 5.1 + 124 = 135.9

L = 135.9