MATH SOLVE

4 months ago

Q:
# Assume the readings on thermometers are normally distributed with a mean of 0degreesC and a standard deviation of 1.00degreesC. Find the probability that a randomly selected thermometer reads between negative 1.52 and negative 0.81 and draw a sketch of the region.

Accepted Solution

A:

Answer:Step-by-step explanation:Given : The readings on thermometers are normally distributed withMean : [tex]\mu=\ 0[/tex]Standard deviation : [tex]\sigma= 1[/tex]The formula to calculate the z-score :-[tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x = -1.52[tex]z=\dfrac{-1.52-0}{1}=-1.52[/tex]For x = -0.81[tex]z=\dfrac{-0.81-0}{1}=-0.81[/tex]The p-value = [tex]P(-1.52<z<-0.81)=P(z<-0.81)-P(z<-1.52)[/tex][tex]0.2089701-0.0642555=0.1447146\approx0.1447[/tex]Hence, the probability that a randomly selected thermometer reads between negative 1.52 and negative 0.81 = 0.1447