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

`X_(1)=1.23`

Step-by-step 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 ( (X-N)/(\sigma ) >(X_(1)-0)/(1)\right )=0.89`

`P\left ( Z>Z_(1) )=0.89`

Now using Normal table, Z = 1.23

Therefore,
`(X_(1)-0)/(1)=1.23`

`X_(1)=1.23`