Question

A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 89​, the 89 th percentile. This is the temperature reading separating the bottom 89 % from the top 11 %.

Answer 1

Answer:

$X_{1}=1.23$

Explanation:

Given :

μ = 0

σ = 1

For 89th percentile

using invariant norm ( area, μ, σ )

       = inv. norm ( 0.89, 0, 1 )

       = 1.23

or

P ( x > $X_{1}$ ) = 0.89

$P\left ( \frac{X-N}{\sigma } >\frac{X_{1}-0}{1}\right )=0.89$

$P\left ( Z>Z_{1} )=0.89$

Now using Normal table, Z = 1.23

Therefore, $\frac{X_{1}-0}{1}=1.23$

$X_{1}=1.23$