Question

Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of O'C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -0.972°C. P(Z > - 0.972) =

Answer 1

1) We have ,

$P(Z>-0.972)=1-P(Z\leq -0.972)=1-\Phi(-0.972)=1-[1-\Phi(0.972)]$

$=\Phi(0.972)=0.8340$ ; From standard normal distribution table

2) We have ,

$P(Z>c)=0.0143\Rightarrow 1-P(Z\leq c)=0.0143$

$\Rightarrow 1-\Phi( c)=0.0143$

$\Rightarrow \Phi( c)=1-0.0143=0.9857$...............(I)

From standard normal distribution table , $\Phi( 2.19)=0.9857$ ...............(II)

From (I) and (II) , we get ,

$c=2.19^0C$